chapter_3/serial_chase_exercise.ipynb

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    "import math\n",
    "\n",
    "def distance(a, b):\n",
    "    return math.sqrt((b[0] - a[0]) ** 2 + (b[1] - a[1]) ** 2)\n",
    "\n",
    "# Initialize the Position\n",
    "a = (10, 10)\n",
    "b = (30, 10)\n",
    "c = (30, 30)\n",
    "d = (10, 30)\n",
    "target = (30, 50)\n",
    "\n",
    "# Initialize the velocities\n",
    "va = 35\n",
    "vb = 25\n",
    "vc = 15\n",
    "vd = 10\n",
    "\n",
    "# Initialize the time and time increment\n",
    "time = 0\n",
    "delt = 0.001\n",
    "\n",
    "print(\"   t           A                B                C               D\")\n",
    "print(\"--------------------------------------------------------------------------\")\n",
    "\n",
    "while True:\n",
    "    # Calculate the distances between the objects\n",
    "    distance_AB = distance(a, b)\n",
    "    distance_BC = distance(b, c)\n",
    "    distance_CD = distance(c, d)\n",
    "    distance_DC = distance(d, target)\n",
    "\n",
    "    # Update the positions of the objects\n",
    "    a = (a[0] + va * delt * (b[0] - a[0]) / distance_AB, a[1] + va * delt * (b[1] - a[1]) / distance_AB)\n",
    "    b = (b[0] - vb * delt * (b[0] - c[0]) / distance_BC, b[1] + vb * delt * (c[1] - b[1]) / distance_BC)\n",
    "    c = (c[0] - vc * delt * (c[0] - d[0]) / distance_CD, c[1] - vc * delt * (c[1] - d[1]) / distance_CD)\n",
    "    d = (d[0] + vd * delt * (target[0] - d[0]) / distance_DC, d[1] + vd * delt * (target[1] - d[1]) / distance_DC)\n",
    "\n",
    "    \n",
    "    print(f\"{time:.3f}   {a[0]:.3f}, {a[1]:.3f}   {b[0]:.3f}, {b[1]:.3f}   {c[0]:.3f}, {c[1]:.3f}   {d[0]:.3f}, {d[1]:.3f}\")\n",
    "\n",
    "\n",
    "    # Check if any of the objects have been hit\n",
    "    if distance_AB < 0.005:\n",
    "        print(\"A hits B\")\n",
    "        break\n",
    "    elif distance_BC < 0.005:\n",
    "        print(\"B hits C\")\n",
    "        break\n",
    "    elif distance_CD < 0.005:\n",
    "        print(\"C hits D\")\n",
    "        break\n",
    "    elif distance_DC < 0.005:\n",
    "        print(\"D hits A\")\n",
    "        break\n",
    "\n",
    "    # Increase the time\n",
    "    time += delt\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def distance(a, b):\n",
    "    return math.sqrt((b[0] - a[0]) ** 2 + (b[1] - a[1]) ** 2)\n",
    "\n",
    "# Initialize the Position\n",
    "a = (10, 10)\n",
    "b = (30, 10)\n",
    "c = (30, 30)\n",
    "d = (10, 30)\n",
    "target = (30, 50)\n",
    "\n",
    "# Initialize the velocities\n",
    "va = 35\n",
    "vb = 25\n",
    "vc = 15\n",
    "vd = 10\n",
    "\n",
    "# Initialize the time and time increment\n",
    "time = 0\n",
    "delt = 0.001\n",
    "\n",
    "# Create empty lists to store the positions\n",
    "path_a = [a]\n",
    "path_b = [b]\n",
    "path_c = [c]\n",
    "path_d = [d]\n",
    "\n",
    "print(\"   t           A                B                C               D\")\n",
    "print(\"--------------------------------------------------------------------------\")\n",
    "\n",
    "while True:\n",
    "    # Calculate the distances between the objects\n",
    "    distance_AB = distance(a, b)\n",
    "    distance_BC = distance(b, c)\n",
    "    distance_CD = distance(c, d)\n",
    "    distance_DC = distance(d, target)\n",
    "\n",
    "    # Update the positions of the objects\n",
    "    a = (a[0] + va * delt * (b[0] - a[0]) / distance_AB, a[1] + va * delt * (b[1] - a[1]) / distance_AB)\n",
    "    b = (b[0] - vb * delt * (b[0] - c[0]) / distance_BC, b[1] + vb * delt * (c[1] - b[1]) / distance_BC)\n",
    "    c = (c[0] - vc * delt * (c[0] - d[0]) / distance_CD, c[1] - vc * delt * (c[1] - d[1]) / distance_CD)\n",
    "    d = (d[0] + vd * delt * (target[0] - d[0]) / distance_DC, d[1] + vd * delt * (target[1] - d[1]) / distance_DC)\n",
    "    \n",
    "    \n",
    "    # Append the positions to the path lists\n",
    "    path_a.append(a)\n",
    "    path_b.append(b)\n",
    "    path_c.append(c)\n",
    "    path_d.append(d)\n",
    "    \n",
    "    print(f\"{time:.3f}   {a[0]:.3f}, {a[1]:.3f}   {b[0]:.3f}, {b[1]:.3f}   {c[0]:.3f}, {c[1]:.3f}   {d[0]:.3f}, {d[1]:.3f}\")\n",
    "\n",
    "\n",
    "    # Check if any of the objects have been hit\n",
    "    if distance_AB < 0.005:\n",
    "        print(\"A hits B\")\n",
    "        break\n",
    "    elif distance_BC < 0.005:\n",
    "        print(\"B hits C\")\n",
    "        break\n",
    "    elif distance_CD < 0.005:\n",
    "        print(\"C hits D\")\n",
    "        break\n",
    "    elif distance_DC < 0.005:\n",
    "        print(\"D hits A\")\n",
    "        break\n",
    "\n",
    "    # Increase the time\n",
    "    time += delt\n",
    "\n",
    "\n",
    "# Extract x and y coordinates from the path lists\n",
    "path_a_x, path_a_y = zip(*path_a)\n",
    "path_b_x, path_b_y = zip(*path_b)\n",
    "path_c_x, path_c_y = zip(*path_c)\n",
    "path_d_x, path_d_y = zip(*path_d)\n",
    "\n",
    "# Plot the paths\n",
    "plt.plot(path_a_x, path_a_y, label='A')\n",
    "plt.plot(path_b_x, path_b_y, label='B')\n",
    "plt.plot(path_c_x, path_c_y, label='C')\n",
    "plt.plot(path_d_x, path_d_y, label='D')\n",
    "plt.scatter(path_a_x[0], path_a_y[0], color='red', marker='o', label='Start')\n",
    "plt.scatter(path_a_x[-1], path_a_y[-1], color='green', marker='o', label='End')\n",
    "plt.scatter(path_b_x[0], path_b_y[0], color='red', marker='o')\n",
    "plt.scatter(path_b_x[-1], path_b_y[-1], color='green', marker='o')\n",
    "plt.scatter(path_c_x[0], path_c_y[0], color='red', marker='o')\n",
    "plt.scatter(path_c_x[-1], path_c_y[-1], color='green', marker='o')\n",
    "plt.scatter(path_d_x[0], path_d_y[0], color='red', marker='o')\n",
    "plt.scatter(path_d_x[-1], path_d_y[-1], color='green', marker='o')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.title('Object Paths')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show()\n"
   ]
  }
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