FinalReportPythonNB.ipynb

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   "attachments": {},
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   "source": [
    "<p style=\"color:#03b5fc; font-size:60px;\">HOMOGENOUS COORDINATES</p>"
   ]
  },
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   "attachments": {},
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   "metadata": {},
   "source": [
    "* Homogenous co-ordinates are a mathematical representation used in projective geometry & Computer Graphics\n",
    "\n",
    "* They provide a way to represent points, vectors & transformations in a uniform manner\n",
    "\n",
    "* We extend the Cartesian system by using an additional coordinate usually denoted as `\"w\"`\n",
    "\n",
    "A point in Homogenous system is represented as \n",
    "$$(x, y, z, w)$$ \n",
    "$$where\\ (x, y, z)\\ are\\ the\\ cartesian\\ coordinates$$\n",
    "\n",
    "`\"w\"` is called the `\"Scaling factor\"`"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style=\"color:#03b5fc; font-size:60px;\">GEOMETRIC TRANSFORMATIONS</p>"
   ]
  },
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   "attachments": {},
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   "metadata": {},
   "source": [
    "* There are several types of geometric transformations:\n",
    "    * `Translation`\n",
    "    * `Rotation`\n",
    "    * `Scaling`\n",
    "    * `Shearing`\n",
    "    * `Reflection`\n",
    "    * `Projection`\n",
    "<br>\n",
    "<br>\n",
    "\n",
    "* These tranformations can be applied individually or in combinations in order to achieve better effects\n",
    "\n",
    "* They are widely used in fields like `Computer Graphics`, `Compiter Vision`, `Designing & modelling` etc.\n",
    "\n",
    "* We will be particularly discussing about translation, rotation and scaling"
   ]
  },
  {
   "attachments": {},
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   "metadata": {},
   "source": [
    "<p style=\"color:#03b5fc; font-size:60px;\">TRANSLATION</p>"
   ]
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   "attachments": {},
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   "source": [
    "* Translation refers to moving of an object in a certain direction without changing its `size/shape`\n",
    "\n",
    "* It is done by adding constant values to the coordinates of the object"
   ]
  },
  {
   "attachments": {},
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   "metadata": {},
   "source": [
    "Lets say working with a 2D system, we have an object's coordinates as $\\begin{pmatrix}x & y\\\\\\end{pmatrix}$\n",
    "<br>\n",
    "<br>\n",
    "<br>\n",
    "Thus, in Homogenous coordinates, we can represent it as $\\begin{pmatrix}x & y & 1\\\\\\end{pmatrix} = V$\n",
    "<br>\n",
    "<br>\n",
    "<br>\n",
    "Further, lets say we want to translate this position vector by $2\\ units\\ in\\ +x\\ and\\ 1\\ unit\\ in\\ -y$ \n",
    "<br>\n",
    "<br>\n",
    "<br>\n",
    "Then we can make a respective `\"translation matrix\"` using the homogenous coordinates called `T` such that:\n",
    "\n",
    "$$V*T = V'$$\n",
    "\n",
    "$$(where\\ V'\\ represents\\ the\\ final\\ homogenous\\ coordinates\\ after\\ translation)$$\n",
    "\n",
    "Thus, we can represent `T` as:\n",
    "$$T = \\begin{pmatrix}\n",
    "1 & 0 & 0 \\\\\n",
    "0 & 1 & 0 \\\\\n",
    "t_x & t_y & 1\\\\\n",
    "\\end{pmatrix}$$\n",
    "\n",
    "<br>\n",
    "\n",
    "$$here,\\ (t_x = 2)\\ \\&\\ (t_y = -1)$$\n",
    "\n",
    "\n",
    "This makes the final equation for a single translation as:\n",
    "\n",
    "$$\\begin{pmatrix}\n",
    "x & y & 1 \\\\\n",
    "\\end{pmatrix}\n",
    "\\begin{pmatrix}\n",
    "1 & 0 & 0 \\\\\n",
    "0 & 1 & 0 \\\\\n",
    "t_x & t_y & 1\\\\\n",
    "\\end{pmatrix} = \n",
    "\\begin{pmatrix}\n",
    "x' & y' & 1 \\\\\n",
    "\\end{pmatrix}$$\n",
    "\n",
    "<br>\n",
    "\n",
    "Similarly, if we have to perform 3 translations, namely $T_1,\\ T_2\\ and\\ T_3$ then we can write the final homo-coords as V':\n",
    "\n",
    "$$V*T_f = V'$$\n",
    "\n",
    "Here, $T_f\\ =\\ (T_1*T_2*T_3)$\n",
    "\n",
    "And each $T_i$ represents the respective translation matrix for $i^{th}$ translation"
   ]
  },
  {
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   "source": [
    "<p style=\"color:#03b5fc; font-size:60px;\">ROTATION</p>"
   ]
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   "source": [
    "* Rotation as a transformation involves rotating an object around a fixed point or axis\n",
    "\n",
    "* `Size/shape` of the object is preserved"
   ]
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   "source": [
    "Very much similar to translation, a rotation can also be represented in homogenous coordinates as a matrix\n",
    "\n",
    "$$\n",
    "R = \\begin{pmatrix}\n",
    "cos\\theta & sin\\theta & 0 \\\\\n",
    "-sin\\theta & cos\\theta & 0 \\\\\n",
    "0 & 0 & 1 \\\\\n",
    "\\end{pmatrix}$$\n",
    "\n",
    "$$\\theta\\ represents\\ angle\\ by\\ which\\ it\\ is\\ rotated$$\n",
    "\n",
    "<br>\n",
    "\n",
    "Thus, if an object with homogenous coordinates $\\begin{pmatrix}x & y & 1\\\\\\end{pmatrix}$ is to be rotated by $\\theta$ angle:\n",
    "\n",
    "$$V*R = V'$$\n",
    "$$(V'\\ represents\\ final\\ homogenous\\ coordinates)$$\n",
    "\n",
    "<br>\n",
    "\n",
    "$$\\begin{pmatrix}\n",
    "x & y & 1\\\\\n",
    "\\end{pmatrix}\n",
    "\\begin{pmatrix}\n",
    "cos\\theta & sin\\theta & 0\\\\\n",
    "-sin\\theta & cos\\theta & 0\\\\\n",
    "0 & 0 & 1\\\\\n",
    "\\end{pmatrix} = \n",
    "\\begin{pmatrix}\n",
    "x' & y' & 1\\\\\n",
    "\\end{pmatrix}$$\n",
    "\n",
    "<br>\n",
    "\n",
    "And also similar to translation, multiple rotations can be handled by finding a `FINAL` rotation matrix which is then multiplied with the homogenous coordinates"
   ]
  },
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   "source": [
    "<p style=\"color:#03b5fc; font-size:60px;\">SCALING</p>"
   ]
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   "source": [
    "* Scaling leads to change in the `size` if the object by either enlarging or shrinking the object\n",
    "\n",
    "* This achieved by multiplying the coordinates of the vector by a scalar value"
   ]
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   "source": [
    "Scaling is also done in the same way. We can denote the scaling factors in a matrix form as:\n",
    "\n",
    "$$\n",
    "S = \\begin{pmatrix}\n",
    "S_x & 0 & 0\\\\\n",
    "0 & S_y & 0\\\\\n",
    "0 & 0 & 1\\\\\n",
    "\\end{pmatrix}$$\n",
    "$$(S_x = scaling\\ along\\ x\\ axis)$$\n",
    "$$(S_y = scaling\\ along\\ y\\ axis)$$\n",
    "\n",
    "<br>\n",
    "\n",
    "Thus, say a position coordinate $\\begin{pmatrix}x & y & 1\\\\\\end{pmatrix}$ is undergoing scaling\n",
    "\n",
    "\n",
    "It is enlarged to twice its size along $x\\ axis$ while halved along $y\\ axis$\n",
    "\n",
    "\n",
    "\n",
    "So $S_x = 2$ while $S_y = 0.5$\n",
    "\n",
    "$$\n",
    "\\begin{pmatrix}\n",
    "x & y & 1\\\\\n",
    "\\end{pmatrix}\n",
    "\\begin{pmatrix}\n",
    "S_x & 0 & 0\\\\\n",
    "0 & S_y & 0\\\\\n",
    "0 & 0 & 1\\\\\n",
    "\\end{pmatrix} = \n",
    "\\begin{pmatrix}\n",
    "x' & y' & 1\\\\\n",
    "\\end{pmatrix}\n",
    "$$\n",
    "\n",
    "<br>\n",
    "\n",
    "The above calculation provides us with the final homogenoues coordinates of the object after scaling"
   ]
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   "source": [
    "<p style=\"color:#03b5fc; font-size:60px;\">EXAMPLE</p>"
   ]
  },
  {
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style=\"color:#73fc03; font-size:40px;\">Question</p>"
   ]
  },
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   "attachments": {},
   "cell_type": "markdown",
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   "source": [
    "Say there is a square ABCD such that $A(1,1)$ $B(3,1)$ $C(3,3)$ $D(1,3)$ and its centre is at $E(2,2)$\n",
    "\n",
    "We need to perform a set of geometrical transformations on the square\n",
    "\n",
    "* The final object should be a square with thrice its original side length \n",
    "* It sholuld also be rotated $90 \\degree$ clockwise\n",
    "* Its centre should stay at same $E(2,2)$\n",
    "\n",
    "Find the resultant `\"transformation matrix\"` for the above changes and also find all the final coordinates"
   ]
  },
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   "source": [
    "<p style=\"color:#73fc03; font-size:40px;\">Solution</p>"
   ]
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   "source": [
    "* We first need to plan it step-wise:\n",
    "\n",
    "    * translating the sqaure such that the centre is at Origin\n",
    "    * scaling the square to 3 times its size in x as well as y axis\n",
    "    * rotating the whole square by -90 deg (since clockwise rotation)\n",
    "    * translating it back such that new centre at original (2,2) coordinates\n",
    "\n",
    "<br>\n",
    "\n",
    "* Thus, there will be $T_1$ matirix for $step_1$ `translation`, $S$ for $step_2$ `scaling`, $R$ for $step_3$ `rotation` and then finally $T_2$ for $step_4$ `translation`\n",
    "\n",
    "<br>\n",
    "\n",
    "Putting down values of the matrices mentioned above:\n",
    "\n",
    "$$\n",
    "T_1 = \\begin{pmatrix}\n",
    "1 & 0 & 0\\\\\n",
    "0 & 1 & 0\\\\\n",
    "-2 & -2 & 1\\\\\n",
    "\\end{pmatrix}$$\n",
    "\n",
    "$$\n",
    "S = \\begin{pmatrix}\n",
    "3 & 0 & 0\\\\\n",
    "0 & 3 & 0\\\\\n",
    "0 & 0 & 1\\\\\n",
    "\\end{pmatrix}$$\n",
    "\n",
    "$$\n",
    "R = \\begin{pmatrix}\n",
    "0 & -1 & 0\\\\\n",
    "1 & 0 & 0\\\\\n",
    "0 & 0 & 1\\\\\n",
    "\\end{pmatrix}$$\n",
    "\n",
    "$$\n",
    "T_2 = \\begin{pmatrix}\n",
    "1 & 0 & 0\\\\\n",
    "0 & 1 & 0\\\\\n",
    "2 & 2 & 1\\\\\n",
    "\\end{pmatrix}$$\n",
    "\n",
    "<br>\n",
    "\n",
    "Now, we can also represent the 4 coordinates altogether in one single matrix to reduce the number of steps\n",
    "\n",
    "$$\n",
    "M = \\begin{pmatrix}\n",
    "A\\\\\n",
    "B\\\\\n",
    "C\\\\\n",
    "D\\\\\n",
    "\\end{pmatrix}$$\n",
    "\n",
    "<br>\n",
    "\n",
    "$$after\\ expanding\\ M = \n",
    "\\begin{pmatrix}\n",
    "1 & 1 & 1\\\\\n",
    "3 & 1 & 1\\\\\n",
    "1 & 3 & 1\\\\\n",
    "\\end{pmatrix}$$\n",
    "\n",
    "<br>\n",
    "\n",
    "Further, we can find the resultant transformation matrix:\n",
    "    $$result = T_1*S*R*T_2$$\n",
    "    \n",
    "$$\n",
    "result = \\begin{pmatrix}\n",
    "0 & -3 & 0\\\\\n",
    "3 & 0 & 0\\\\\n",
    "-4 & 8 & 1\\\\\n",
    "\\end{pmatrix}$$\n",
    "\n",
    "<br>\n",
    "\n",
    "Last step in the method is to find the final coordinate matrix $M'$\n",
    "\n",
    "$$M*result = M'$$\n",
    "\n",
    "$$\n",
    "\\begin{pmatrix}\n",
    "1 & 1 & 1\\\\\n",
    "3 & 1 & 1\\\\\n",
    "3 & 3 & 1\\\\\n",
    "1 & 3 & 1\\\\\n",
    "\\end{pmatrix}\n",
    "\\begin{pmatrix}\n",
    "0 & -3 & 0\\\\\n",
    "3 & 0 & 0\\\\\n",
    "-4 & 8 & 1\\\\\n",
    "\\end{pmatrix} = \n",
    "\\begin{pmatrix}\n",
    "-1 & 5 & 1\\\\\n",
    "-1 & -1 & 1\\\\\n",
    "5 & -1 & 1\\\\\n",
    "5 & 5 & 1\\\\\n",
    "\\end{pmatrix} = M'\n",
    "$$\n",
    "\n",
    "<br>\n",
    "\n",
    "Hence, from the final coordinate matrix $M'$ that is formed, we can get the new cartesian coordinates of the vertices\n",
    "\n",
    "$A'(-1, 5)\\ B'(-1, -1)\\ C'(5, -1)\\ D'(5, 5)$\n",
    "\n",
    "<br>\n",
    "\n",
    "While, if we find the centre of the new coordinates, it still comes out to be $E(2, 2)$\n",
    "\n",
    "So this also proves that our method has worked.\n",
    "\n",
    "<br>\n",
    "\n",
    "Plus, intial edge length was 2\n",
    "\n",
    "Whereas now, it is 6 so the whole square is scaled to thrice its size"
   ]
  },
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   "metadata": {},
   "source": [
    "<p style=\"color:#03b5fc; font-size:60px;\">WHY HOMOGENOUS COORDINATES?</p>"
   ]
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   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Consider a set of 2D points that need to be rotated about an axis by a certain angle. Such type of `Geometric transformations` are very much needed in today's world in a variety of fields like Computer Graphics, Robotics, 3D modeling, Medical industry, blueprint designing, etc.\n",
    "\n",
    "* Thus, we can use Homogenous Coordinates in these fields in order to simplify the working mechanisms while motivating us to create and innovate better ideas & concepts using such mathematical tools.\n",
    "\n",
    "* Further, we will dive deeper into some of the fields, namely:\n",
    "    * `Computer Graphics`\n",
    "    * `Medical Imaging`"
   ]
  },
  {
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   "metadata": {},
   "source": [
    "<p style=\"color:#03b5fc; font-size:60px;\">COMPUTER GRAPHICS</p>"
   ]
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   "source": [
    "* Homogenous coordinates play a vital role in Computer Graphics as they are used to like a unified framework for representing points, lines and transformations\n",
    "\n",
    "* They can be used to create stunning visual effects, scenes & animations\n",
    "\n",
    "* They enable efficient rendering of 3D objects as well as handling of prespective projection\n",
    "\n",
    "The above are some of the numerous concepts in Computer Graphics (CG).\n",
    "\n",
    "We will now discuss about a similar concept in Computer Graphics called `Heirarchical Modeling`."
   ]
  },
  {
   "attachments": {},
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   "metadata": {},
   "source": [
    "<p style=\"color:#03b5fc; font-size:60px;\">HEIRARCHICAL MODELING</p>"
   ]
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   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Heirarchical modeling refers to the method of building & representing complex scenes from very simple shapes.\n",
    "\n",
    "The key is that a complex object can be made up of relatively simpler objects, which in turn can be made using even simpler objects and so on.... until it all bottoms out to `SIMPLE GEOMETRIC SHAPES` like circles, rectangles etc."
   ]
  },
  {
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   "source": [
    "<p style=\"color:#73fc03; font-size:40px;\">Application of HomoCoords</p>"
   ]
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   "source": [
    "* Major motivation for introducing a new coordinate system is that it should make it possible for us to use the system that is most natural to the scene that you want to draw \n",
    "\n",
    "* We can extend this idea to individual objects in a scene: when drawing an object, use the coordinate system that is most natural for that particular object\n",
    "\n",
    "* For selecting the system, it is most natural for an object to be cantred at Origin $(0, 0)$ or use it as a convenient reference point. Thus, we can proceed with that system for all the objects included in a scene initially\n",
    "\n",
    "* Further, at the time of merging all the objects altogether in the scene, we can simply use `scaling`, `rotation` followed by `translation` geometric transformations\n",
    "\n",
    "* This is done in order to set their size, orientation & position according to the scene's requirement. This is also known as $Modeling\\ Transformation$\n",
    "\n",
    "* The transformations are done in the same order as mentioned since first 2 operations dont change the reference point. Thus, the changing of reference point could be done at the last without any discrepancies\n",
    "\n",
    "<br>\n",
    "\n",
    "The modeling transformations that are used to place an object in the scene should not affect other objects in the scene. So to limit their application to just the one object, we can save the current transformation before starting work on the object and restore it afterwards\n",
    "\n",
    "Let's suppose here that there are subroutines $saveTransform()$ and $restoreTransform()$ for performing those tasks\n",
    "\n",
    "Here, `saveTransform` will make a copy of the modeling transformation that is currently in effect and store that copy while it does not change the current transformation \n",
    "\n",
    "Later, when `restoreTransform` is called, it will retrieve that copy and will replace the current modeling transform with the retrieved transform.\n",
    "\n",
    "Typical code for drawing an object will then have the form:\n",
    "\n",
    "$saveTransform()\\\\$\n",
    "$translate(dx,dy)\\\\$\n",
    "$rotate(r)\\\\$\n",
    "$scale(sx,sy)\\\\$\n",
    "$     .\\\\$\n",
    "$     .\\ ->draw\\ the\\ object\\ with\\ natural\\ coordinates\\\\$\n",
    "$     .\\\\$\n",
    "$restoreTransform()\\\\$"
   ]
  },
  {
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   "source": [
    "<p style=\"color:#73fc03; font-size:40px;\">Working Methodology</p>"
   ]
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   "source": [
    "* Now, we can extend the above idea on a complex scene, let's say for example, a system containing a potted flower. This system can be broken down into smaller systems as pot, stem, leaves and bloom\n",
    "\n",
    "* Further, taking say the bloom, it can be made up different petals of different shapes and sizes\n",
    "\n",
    "* Even further, each petal can be created using simple geometrical shapes like circles, ellipses, etc. in its own natural coordinate system centred at Origin $(0, 0)$\n",
    "\n",
    "* After that, merging things step-by-step, we will first apply `Modeling transformations` on each of the petals to make the bloom overall\n",
    "\n",
    "* Further, we can apply modeling transformations on the whole bloom, stem, leaves as well as the pot and merge them to make the flower\n",
    "\n",
    "* And at the end, we can apply modeling transformation on the complete flower to places it into the designed scene with background"
   ]
  },
  {
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   "source": [
    "<p style=\"color:#73fc03; font-size:40px;\">Example</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# for QR codes use inline\n",
    "%matplotlib inline\n",
    "#\n",
    "# for lecture use notebook\n",
    "# %matplotlib notebook\n",
    "# qr_setting = None\n",
    "#\n",
    "%config InlineBackend.figure_format='retina'\n",
    "# import libraries\n",
    "import numpy as np\n",
    "import matplotlib as mp\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "# import laUtilities as ut\n",
    "# import slideUtilities as sl\n",
    "# import demoUtilities as dm\n",
    "import pandas as pd\n",
    "from importlib import reload\n",
    "from datetime import datetime\n",
    "from IPython.display import Image\n",
    "from IPython.display import display_html\n",
    "from IPython.display import display\n",
    "from IPython.display import Math\n",
    "from IPython.display import Latex\n",
    "from IPython.display import HTML\n",
    "from IPython.display import YouTubeVideo\n",
    "from IPython.display import Audio\n",
    "# reload(sl)\n",
    "# reload(ut)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# set up view\n",
    "import matplotlib.animation as animation\n",
    "mp.rcParams['animation.html'] = 'jshtml'\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = plt.axes(xlim=(-5,5),ylim=(-5,5))\n",
    "plt.plot(-2,-2,'')\n",
    "plt.plot(2,2,'')\n",
    "plt.axis('equal')\n",
    "ballLines = []\n",
    "for b in ball:\n",
    "    ballLines += ax.plot([],[])\n",
    "plt.close()\n",
    "#\n",
    "#to get additional args to animate:\n",
    "#def animate(angle, *fargs):\n",
    "#    fargs[0].view_init(azim=angle)\n",
    "def animate(frame):\n",
    "    angle = 2.0 * np.pi * (frame/100.0)\n",
    "    rotationMatrix = np.array([[np.cos(angle), 0, -np.sin(angle)],\n",
    "                               [0,             1,              0],\n",
    "                               [np.sin(angle), 0, np.cos(angle)]])\n",
    "    for b,l in zip(ball,ballLines):\n",
    "        rb = rotationMatrix @ b\n",
    "        l.set_data(rb[0],rb[1])\n",
    "    fig.canvas.draw()\n",
    "#\n",
    "# create the animation \n",
    "animation.FuncAnimation(fig, animate,\n",
    "                       frames=np.arange(0,100,1),\n",
    "                       fargs=None,\n",
    "                       interval=100,\n",
    "                       repeat=True)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$The\\ above\\ code\\ creates\\ a\\ rotating\\ ball\\ as\\ shown$$"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# set up view\n",
    "import matplotlib.animation as animation\n",
    "mp.rcParams['animation.html'] = 'jshtml'\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = plt.axes(xlim=(-5,5),ylim=(-5,5))\n",
    "plt.plot(-2,-2,'')\n",
    "plt.plot(2,2,'')\n",
    "plt.axis('equal')\n",
    "with open('cube.obj','r') as fp:\n",
    "    cube = obj.obj2flist(fp)\n",
    "cube = obj.homogenize(cube)\n",
    "cubeLines = []\n",
    "for c in cube:\n",
    "    cubeLines += ax.plot([],[])\n",
    "#\n",
    "def animate(i):\n",
    "    angle = 2.0 * np.pi * (i/100.0)\n",
    "    P = np.array([[1.,0,0,0],[0,1.,0,0],[0,0,0,0],[0,0,-1./8,1]]).dot(np.array([[np.cos(angle),0,-np.sin(angle),0],[0,1,0,0],[np.sin(angle),0,np.cos(angle),0],[0,0,0,1]]))\n",
    "    for b,l in zip(cube,cubeLines):\n",
    "        rb = P.dot(b)\n",
    "        l.set_data(rb[0]/rb[3],rb[1]/rb[3])\n",
    "    fig.canvas.draw()\n",
    "#\n",
    "# create the animation \n",
    "animation.FuncAnimation(fig, animate,\n",
    "                       frames=np.arange(0,100,1),\n",
    "                       fargs=None,\n",
    "                       interval=100,\n",
    "                       repeat=False)\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$The\\ above\\ code\\ creates\\ an\\ animation\\ of\\ a\\ rotating\\ cube$$"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style=\"color:#03b5fc; font-size:60px;\">MEDICAL IMAGING</p>"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Medical Science, especially `Medical Imaging` is one of things that has always had huge roles of Homogenous Coordinates in various fields\n",
    "\n",
    "* Fields that involve `image visualization` and especially modern medical fields like radiology work using processes that are primarily based on Linear Algebraic transformations\n",
    "\n",
    "* `Tomographic Recontruction` is one of the methods used in modern Medical Science for `Computed Tomography(CT) scans`\n",
    "\n",
    "* Thus, we will now be discussing about the concept of `Tomography` in regards with Medical Imaging"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style=\"color:#03b5fc; font-size:60px;\">TOMOGRAPHY</p>"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Tomography is the idea or concept of reconstruction of an object via obtaining the object in terms of slices\n",
    "\n",
    "* We do this procedure with humans using `photons`. We pass them through a human body part and upon doing, so we can study the `rates absorption of photons`\n",
    "\n",
    "* Its analogue (signal info) would be akin to studying an object from its shadow, from various heights. The phenomenon used here is something called `attenuation`\n",
    "\n",
    "* We pass X-rays through the human body and at every point, we measure the intensities of these X-rays after they pass out through the body\n",
    "\n",
    "* Thus, with different heights or layers of the body part, after passage of photons, will lead to shadows of different intensities. This helps in creating the final projected image of the body part"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style=\"color:#73fc03; font-size:40px;\">Applications of HomoCoords</p>"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Homogenous Coordinates are simply the very basis of tomography. We obtain various projections of an image and from those projections, we apply a linear combination of them to reconstruct something similar to the original image\n",
    "\n",
    "* Thus, 2 major HomoCoords applications are present in tomography, namely: `scaling & projections`\n",
    "\n",
    "* Additionally, one of the major facets of tomographic reconstructions, which is `Volume Rendering`, that transforms a set of 2D images into a 3D object is done using geometric transformations and HomoCoords\n",
    "\n",
    "* Reconstructions can also be used to transform the dimensions of the already obtained objects. Basically, using a combination of lower dimensional slices to reconstruct a higher dimensional object"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style=\"color:#73fc03; font-size:40px;\">Working Methodology</p>"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "CT constructions are obtained via getting `multiple slices`. Each slice would look something like the image shown below"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Now, we can study each of these slices individually. We can represent each slice as a grid/matrix of pixels. Also, each of those pixels will be having a certain intensity\n",
    "\n",
    "* A sample visualization of the grid is as shown below"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The photons contituting the X-Ray beam are absorbed by the tissue within the pixel at a rate proportional to the X-Ray density of the tissue\n",
    "\n",
    "* Quantitatively, the X-Ray density of the $i^{th}$ pixel is denoted by $X_i$ and is defined by the given formula below:\n",
    "\n",
    "$$X_i = \\log_{10}(fraction\\ of\\ photons\\ passing\\ through\\ i^{th}\\ pixel\\ without\\ being\\ absorbed)$$\n",
    "\n",
    "<br>\n",
    "\n",
    "Now, since log function are aditive, so we have:\n",
    "\n",
    "$$X_1 + X_2 + X_3 + ........ + X_n = \\log_{10}(total\\ fraction\\ of\\ photons\\ passing\\ through\\ a\\ row\\ of\\ n\\ photons)$$\n",
    "\n",
    "<br>\n",
    "\n",
    "Further, lets have a look at each of the beams:\n",
    "* In a CT scan machine, we can have 2 main things, namely: `emitters & receptors`. There is an array of receptors, each obtaining an intensity of a beam\n",
    "\n",
    "* Since we obviously know the intensity of the beam when its produced, we can obtain the relative change in intensity of the beam as some contant $B_i$\n",
    "\n",
    "* Thus, we have these values and can use them as the solutions to the above equations as:\n",
    "\n",
    "$$X_1 + X_2 + X_3 + ........ + X_n = B_i$$\n",
    "\n",
    "<br>\n",
    "\n",
    "However, the projections that we obtain are for various angles and are definitely not only linear. Thus, what we actually obtain is a `LINEAR COMBINATION` of these pixels:\n",
    "\n",
    "$$A_{i1}X_1 + A_{i2}X_2 + A_{i3}X_3 + ......... + A_{in}X_n = B_i$$\n",
    "\n",
    "<br>\n",
    "\n",
    "And thus, we can have $m$ such projections and their respective equations such that $1 \\le i \\le m$:\n",
    "\n",
    "$$A_{11}X_1 + A_{12}X_2 + A_{13}X_3 + ......... + A_{1n}X_n = B_1$$\n",
    "$$A_{21}X_1 + A_{22}X_2 + A_{23}X_3 + ......... + A_{2n}X_n = B_2$$\n",
    "$$*$$\n",
    "$$*$$\n",
    "$$*$$\n",
    "$$*$$\n",
    "$$A_{m1}X_1 + A_{m2}X_2 + A_{m3}X_3 + ......... + A_{mn}X_n = B_m$$\n",
    "\n",
    "<br>\n",
    "\n",
    "$$\"THIS\\ IS\\ SIMPLY\\ A\\ SYSTEM\\ OF\\ LINEAR\\ EQUATIONS!!\"$$\n",
    "\n",
    "<br>\n",
    "\n",
    "* After this, we obtain the images in a slice. These images are further fit together using a method known as `Random Transform`\n",
    "\n",
    "* Although, this method needs us to dive even more deep into medical terminologies as well as mathematics beyond just Linear Algebra and HomoCoords\n",
    "\n",
    "* Thus, we will limit our discussion regarding Medical Imaging till the end of Tomography itself for now"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style=\"color:#73fc03; font-size:40px;\">Example</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import tomopy, dxchange, numpy, h5py, matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "phantom = tomopy.misc.phantom.shepp3d(128)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, (axL, axR) = plt.subplots(1, 2)\n",
    "axL.imshow(phantom[64])\n",
    "axL.set_title(\"XY slice\")\n",
    "axR.imshow(phantom[:,64])\n",
    "axR.set_title(\"XZ slice\")\n",
    "plt.show(block=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "angles = tomopy.sim.project.angles(181)\n",
    "proj = tomopy.sim.project.project(phantom, theta=angles)\n",
    "plt.figure()\n",
    "for i in proj:\n",
    "    plt.imshow(i)\n",
    "    plt.show(block=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import tomopy\n",
    "obj = tomopy.shepp3d() # Generate an object.\n",
    "ang = tomopy.angles(180) # Generate uniformly spaced tilt angles.\n",
    "sim = tomopy.project(obj, ang) # Calculate projections.\n",
    "rec = tomopy.recon(sim, ang, algorithm='art') # Reconstruct object.\n",
    "\n",
    "# Show 64th slice of the reconstructed object.\n",
    "import pylab\n",
    "pylab.imshow(rec[64], cmap='gray')\n",
    "pylab.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The above are `exemplar` images generated using the above code base\n",
    "\n",
    "* The code on running generates huge number of images so we have manually reduced the them and kept them in order such that it is still easy to understand how exactly various slices look like\n",
    "\n",
    "* We can also observe the changing pattern in these images above which represent the gradually changing direction of catching the passed photons"
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
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