Vectors.ipynb

{
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   "source": [
    "import math\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initializing object... \n",
      "x:  0.0\n",
      "y:  4.0\n",
      "z:  5.0\n",
      "self:  {'x': 0.0, 'y': 4.0, 'z': 5.0}\n",
      "Initializing object... \n",
      "x:  1.0\n",
      "y:  7.0\n",
      "z:  6.0\n",
      "self:  {'x': 1.0, 'y': 7.0, 'z': 6.0}\n",
      "Initializing object... \n",
      "x:  0.0\n",
      "y:  5.0\n",
      "z:  9.0\n",
      "self:  {'x': 0.0, 'y': 5.0, 'z': 9.0}\n",
      "Initializing object... \n",
      "x:  1.0\n",
      "y:  7.0\n",
      "z:  2.0\n",
      "self:  {'x': 1.0, 'y': 7.0, 'z': 2.0}\n",
      "__subtract__ method\n",
      "X,Y,Z 1.0 3.0 1.0\n",
      "Initializing object... \n",
      "x:  1.0\n",
      "y:  3.0\n",
      "z:  1.0\n",
      "self:  {'x': 1.0, 'y': 3.0, 'z': 1.0}\n",
      "__subtract__ method\n",
      "X,Y,Z -1.0 -2.0 3.0\n",
      "Initializing object... \n",
      "x:  -1.0\n",
      "y:  -2.0\n",
      "z:  3.0\n",
      "self:  {'x': -1.0, 'y': -2.0, 'z': 3.0}\n",
      "--- CROSS PRODUCT ---\n",
      "Vector u:  [1.0, 3.0, 1.0]\n",
      "Vector v:  [-1.0, -2.0, 3.0]\n",
      "__subtract__ method\n",
      "X,Y,Z -1.0 -2.0 3.0\n",
      "Initializing object... \n",
      "x:  -1.0\n",
      "y:  -2.0\n",
      "z:  3.0\n",
      "self:  {'x': -1.0, 'y': -2.0, 'z': 3.0}\n",
      "__subtract__ method\n",
      "X,Y,Z 1.0 2.0 -7.0\n",
      "Initializing object... \n",
      "x:  1.0\n",
      "y:  2.0\n",
      "z:  -7.0\n",
      "self:  {'x': 1.0, 'y': 2.0, 'z': -7.0}\n",
      "--- CROSS PRODUCT ---\n",
      "Vector u:  [-1.0, -2.0, 3.0]\n",
      "Vector v:  [1.0, 2.0, -7.0]\n"
     ]
    },
    {
     "ename": "AttributeError",
     "evalue": "'NoneType' object has no attribute 'dot'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[1;32m/Users/danieldayto/Coding/algorithms/torc/hackerrank/HackerRank-Solutions/Vectors.ipynb Cell 2'\u001b[0m in \u001b[0;36m<cell line: 64>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     <a href='vscode-notebook-cell:/Users/danieldayto/Coding/algorithms/torc/hackerrank/HackerRank-Solutions/Vectors.ipynb#ch0000003?line=70'>71</a>\u001b[0m x \u001b[39m=\u001b[39m (b \u001b[39m-\u001b[39m a)\u001b[39m.\u001b[39mcross(c \u001b[39m-\u001b[39m b)\n\u001b[1;32m     <a href='vscode-notebook-cell:/Users/danieldayto/Coding/algorithms/torc/hackerrank/HackerRank-Solutions/Vectors.ipynb#ch0000003?line=71'>72</a>\u001b[0m y \u001b[39m=\u001b[39m (c \u001b[39m-\u001b[39m b)\u001b[39m.\u001b[39mcross(d \u001b[39m-\u001b[39m c)\n\u001b[0;32m---> <a href='vscode-notebook-cell:/Users/danieldayto/Coding/algorithms/torc/hackerrank/HackerRank-Solutions/Vectors.ipynb#ch0000003?line=72'>73</a>\u001b[0m angle \u001b[39m=\u001b[39m math\u001b[39m.\u001b[39macos(x\u001b[39m.\u001b[39;49mdot(y) \u001b[39m/\u001b[39m (x\u001b[39m.\u001b[39mabsolute() \u001b[39m*\u001b[39m y\u001b[39m.\u001b[39mabsolute()))\n\u001b[1;32m     <a href='vscode-notebook-cell:/Users/danieldayto/Coding/algorithms/torc/hackerrank/HackerRank-Solutions/Vectors.ipynb#ch0000003?line=74'>75</a>\u001b[0m \u001b[39mprint\u001b[39m(\u001b[39m\"\u001b[39m\u001b[39m%.2f\u001b[39;00m\u001b[39m\"\u001b[39m \u001b[39m%\u001b[39m math\u001b[39m.\u001b[39mdegrees(angle))\n",
      "\u001b[0;31mAttributeError\u001b[0m: 'NoneType' object has no attribute 'dot'"
     ]
    }
   ],
   "source": [
    "\n",
    "class Points(object):\n",
    "    def __init__(self, x, y, z):\n",
    "        print(\"Initializing object... \")\n",
    "        print(\"x: \", x)\n",
    "        print(\"y: \", y)\n",
    "        print(\"z: \", z)\n",
    "        self.x = x\n",
    "        self.y = y\n",
    "        self.z = z\n",
    "        print(\"self: \", self.__dict__)\n",
    "        \n",
    "    def __sub__(self, no):\n",
    "        print(\"__subtract__ method\")\n",
    "        x = self.x - no.x\n",
    "        y = self.y - no.y\n",
    "        z = self.z - no.z\n",
    "        print(\"X,Y,Z\", x,y,z)\n",
    "        return Points(x,y,z)\n",
    "                \n",
    "\n",
    "    def dot(self, no):\n",
    "        u = [self.x, self.y, self.z]\n",
    "        v = [no.x, no.y, no.z]\n",
    "        print(\"Vector u: \", u)\n",
    "        print(\"Vector v: \", v)\n",
    "        dot_product = []\n",
    "        for i in range(3):\n",
    "            dot_product.append(u[i] * v[i])\n",
    "        print(\"dot_product: \", dot_product)\n",
    "        return dot_product    \n",
    "    \n",
    "    # Concept: Create a new vector [cross_x, cross_y, cross_z] \n",
    "    def cross(self, no):\n",
    "        print(\"--- CROSS PRODUCT ---\")\n",
    "        # A(x,y,z) x B(x,y,z)\n",
    "        # X = (A[1]*B[2])-(A[2]*B[1]) \n",
    "        # Y = (A[2]*B[0])-(A[0]*B[2])\n",
    "        # Z = (A[0]*B[1])-(A[1]*B[0])\n",
    "\n",
    "        print(\"self: \", self.__dict__)\n",
    "        print(\"no: \", no)\n",
    "        a = [self.x, self.y, self.z]\n",
    "        b = [no['x'], no['y'], no['z']]\n",
    "        print(\"Vector a: \", a)\n",
    "        print(\"Vector b: \", b)\n",
    "        x = (a[1]*b[2]) - (a[2]*b[1])\n",
    "        y = (a[2]*b[0]) - (a[0]*b[2])\n",
    "        z = (a[0]*b[1]) - (a[1]*b[0])\n",
    "        return Points(x,y,z)\n",
    "        \n",
    "              \n",
    "    def absolute(self):\n",
    "        print(\"--- MAGNITUDE ----\")\n",
    "        print(\"self: \", self.__dict__)\n",
    "        return pow((self.x ** 2 + self.y ** 2 + self.z ** 2), 0.5)\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    points = [[0.0, 4.0, 5.0], [1.0, 7.0, 6.0], [0.0, 5.0, 9.0], [1.0, 7.0, 2.0]]\n",
    "    # points = list()\n",
    "    # for i in range(4):\n",
    "    #     a = list(map(float, input().split()))\n",
    "    #     points.append(a)\n",
    "    a, b, c, d = Points(*points[0]), Points(*points[1]), Points(*points[2]), Points(*points[3])\n",
    "    x = (b - a).cross(c - b)\n",
    "    y = (c - b).cross(d - c)\n",
    "    angle = math.acos(x.dot(y) / (x.absolute() * y.absolute()))\n",
    "\n",
    "    print(\"%.2f\" % math.degrees(angle))"
   ]
  },
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    "\n",
    "# ======== EXAMPLE CASE ========== #    \n",
    "# == INPUTS == #\n",
    "    # 0 4 5 -> A(0,4,5)\n",
    "    # 1 7 6 -> B(1,7,6)\n",
    "    # 0 5 9 -> C(0,5,9)\n",
    "    # 1 7 2 -> D(1,7,2)\n",
    "\n",
    "# PLANE 1 -> (A,B,C)\n",
    "# PLANE 2 -> (B,C,D)\n",
    "\n",
    "# === CALCULATIONS === #\n",
    "    # Angle (PHI)\n",
    "    # Cos(PHI) = (X.Y)/|X||Y|        \n",
    "    # X = AB x BC  \n",
    "        # AB x BC => Cross_Product(AB, BC)\n",
    "            # AB = B - A\n",
    "            # BC = C - B\n",
    "    # Y = BC x CD \n",
    "        # BC x CD => Cross_Product(BC, CD)\n",
    "            # BC = C - B\n",
    "            # CD = D -C\n",
    "    # X.Y -> Dot_Product(X,Y)\n",
    " \n",
    "# === OUTPUT === # \n",
    "    # phi = angle[degrees])\n",
    "        # Degrees displayed using up to two decimal places    \n",
    "\n",
    "# ============= PREREQUISITES ========================== #\n",
    "# --- PREREQUISITE (1): 3D CARTESIAN COORDINATES  ---\n",
    "    # https://www.usna.edu/Users/oceano/raylee/SM223/Ch12_1_Stewart(2016).pdf\n",
    "\n",
    "# --- PREREQUISITE (2): DOT PRODUCT ---\n",
    "    # ---- USE CASES --- #\n",
    "        # (1): Get the angle between two vectors\n",
    "    #  --- CALCULATIONS -- #\n",
    "        # ====== METHOD 1 ====== #\n",
    "        # A.B = |A||B|cos(θ)\n",
    "        # --- EXAMPLE INPUT --- #\n",
    "            # A = [0,4,5]\n",
    "            # B = [1,7,6]\n",
    "                # MAGNITUDE CALCULATION \n",
    "                    # V = (x, y, z) is: |V| = √(x2 + y2 + z2)\n",
    "                        # Step 1 - Find the sum of squares of each component\n",
    "                        # Step 2 - Take the square root of the sum \n",
    "                        # --- EXAMPLE --- #\n",
    "                        # ---- INPUT -- #\n",
    "                            # V = (X,Y,Z)\n",
    "                                # |V| = (x^2 + y^2 + z^2)^1/2\n",
    "            # |B| = Magnitude(Vector B)\n",
    "            # θ = Angle Between Vectors A and B\n",
    "        # ====== METHOD 2 ====== #\n",
    "        # A.B = A1*B1 + A2*B2 + A3*B3 ... \n",
    "            # A = [0,4,5]\n",
    "            # B = [1,7,6]  \n",
    "                # --- FUNCTION --- #\n",
    "                    # DotProduct(A,B)\n",
    "                        # (A[0]*B[0]) + (A[1]*B[1]) + (A[2]*B[2])        \n",
    "                        # (0*1) + (4*7) + (5*6) -> 0 + 28 + 30 = 58\n",
    "        # ===== METHOD 3 ===== #\n",
    "            # A.B = numpy.dot(A,B)\n",
    "\n",
    "                    \n",
    "# --- PREREQUISITE (3): CROSS PRODUCT ---#\n",
    "    # SOURCE: https://betterexplained.com/articles/cross-product/\n",
    "    # ---- USE CASES ---- #\n",
    "        # (1)  Calculate a vector that is perpendicular to two vectors\n",
    "    # --- CALCULATION -- #\n",
    "    #  METHOD 1: A x B = |A||B|sin(theta) \n",
    "            # |A| -> Magnitude (Vector A)\n",
    "            # |B| -> Magnitude (Vector B)\n",
    "            # theta(degrees) --> Angle Between Vectors A and B\n",
    "    # METHOD 2: A x B = \n",
    "        # crossX = vector1.Y * vector2.Z - vector2.Y * vector1.Z\n",
    "        # crossY = -(vector1.X * vector2.Z - vector2.X * vector1.Z)\n",
    "        # crossZ = vector1.X * vector2.Y - vector2.X * vector1.Y\n",
    "        # crossW = 0.0\n",
    "        # --- EXAMPLE ---- # \n",
    "            #  u(1,2,3) x v(4,5,6) = ?\n",
    "                #  ============ MATRIX DETERMINANT CALCULATION ============== #\n",
    "                #                   |  i   j   k  |            |    i  j  k   |\n",
    "                #    u x v    =>    |  u1  u2  u3 |      =>    |    1  2  3   |\n",
    "                #                   |  v1  v2  v3 |            |    4  5  6   | \n",
    "    # METHOD 3: ----- NUMPY OPERATION ------\n",
    "        # FUNCTION --> numpy.cross(a, b)\n",
    "            # a: first vector\n",
    "            # b: second vector\n",
    "    # ==== APPROACH ==== #\n",
    "    # STEP 1: CALCULATE X = (AB x BC)\n",
    "        # (AB x BC) = (B-A) x (C-B)\n",
    "    # ==== EXAMPLE INPUT ==== #    \n",
    "        # 0 4 5 -> A(0,4,5)\n",
    "        # 1 7 6 -> B(1,7,6)\n",
    "        # 0 5 9 -> C(0,5,9)\n",
    "        # 1 7 2 -> D(1,7,2)\n",
    "            # (B-A) = (1-0, 7-4, 6-5) = (1,  3,  1)\n",
    "            # (C-B) = (0-1, 5-7, 9-6) = (-1, -3, 3)\n",
    "                # AB x BC = (1,3,1) x (-1,-3,3)\n",
    "# STEP 2: CALCULATE Y\n",
    "# STEP 3: CALCULATE \n",
    "             "
   ]
  }
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