Computer_Graphics_Practicals.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "67e83ac4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DDA Points: [(1, 1), (2, 2), (3, 3), (4, 3), (5, 4), (6, 5), (7, 6), (8, 6), (9, 7), (10, 8)]\n",
      "Bresenham Points: [(1, 1), (2, 2), (3, 3), (4, 3), (5, 4), (6, 5), (7, 6), (8, 6), (9, 7), (10, 8)]\n"
     ]
    },
    {
     "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": [
    "#1\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def dda_line(x1, y1, x2, y2):\n",
    "    dx = x2 - x1\n",
    "    dy = y2 - y1\n",
    "    steps = abs(dx) if abs(dx) > abs(dy) else abs(dy)\n",
    "    x_increment = dx / steps\n",
    "    y_increment = dy / steps\n",
    "    \n",
    "    x = x1\n",
    "    y = y1\n",
    "    \n",
    "    points = []\n",
    "    points.append((round(x), round(y)))\n",
    "    \n",
    "    for _ in range(steps):\n",
    "        x += x_increment\n",
    "        y += y_increment\n",
    "        points.append((round(x), round(y)))\n",
    "    \n",
    "    return points\n",
    "\n",
    "def bresenham_line(x1, y1, x2, y2):\n",
    "    dx = abs(x2 - x1)\n",
    "    dy = abs(y2 - y1)\n",
    "    steep = dy > dx\n",
    "    \n",
    "    if steep:\n",
    "        x1, y1 = y1, x1\n",
    "        x2, y2 = y2, x2\n",
    "    \n",
    "    if x1 > x2:\n",
    "        x1, x2 = x2, x1\n",
    "        y1, y2 = y2, y1\n",
    "    \n",
    "    dx = abs(x2 - x1)\n",
    "    dy = abs(y2 - y1)\n",
    "    error = dx / 2\n",
    "    y_increment = 1 if y1 < y2 else -1\n",
    "    y = y1\n",
    "    \n",
    "    points = []\n",
    "    \n",
    "    for x in range(x1, x2 + 1):\n",
    "        point = (y, x) if steep else (x, y)\n",
    "        points.append(point)\n",
    "        \n",
    "        error -= dy\n",
    "        if error < 0:\n",
    "            y += y_increment\n",
    "            error += dx\n",
    "    \n",
    "    return points\n",
    "\n",
    "# Test the algorithms\n",
    "x1, y1 = 1, 1\n",
    "x2, y2 = 10, 8\n",
    "\n",
    "# DDA algorithm\n",
    "dda_points = dda_line(x1, y1, x2, y2)\n",
    "print(\"DDA Points:\", dda_points)\n",
    "\n",
    "# Bresenham's algorithm\n",
    "bresenham_points = bresenham_line(x1, y1, x2, y2)\n",
    "print(\"Bresenham Points:\", bresenham_points)\n",
    "\n",
    "# Plotting the lines\n",
    "plt.plot(*zip(*dda_points), marker='o', label='DDA')\n",
    "plt.plot(*zip(*bresenham_points), marker='o', label=\"Bresenham's\")\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "0ef1c54f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Circle Points: [(0, 5), (0, -5), (0, 5), (0, -5), (5, 0), (5, 0), (-5, 0), (-5, 0), (1, 5), (1, -5), (-1, 5), (-1, -5), (5, 1), (5, -1), (-5, 1), (-5, -1), (2, 5), (2, -5), (-2, 5), (-2, -5), (5, 2), (5, -2), (-5, 2), (-5, -2), (3, 4), (3, -4), (-3, 4), (-3, -4), (4, 3), (4, -3), (-4, 3), (-4, -3)]\n"
     ]
    },
    {
     "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": [
    "#2\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def draw_circle(radius):\n",
    "    x = 0\n",
    "    y = radius\n",
    "    d = 1 - radius\n",
    "    delta_e = 3\n",
    "    delta_se = -2 * radius + 5\n",
    "    \n",
    "    points = []\n",
    "    \n",
    "    while y >= x:\n",
    "        points.extend([\n",
    "            (x, y), (x, -y), (-x, y), (-x, -y),\n",
    "            (y, x), (y, -x), (-y, x), (-y, -x)\n",
    "        ])\n",
    "        \n",
    "        if d < 0:\n",
    "            d += delta_e\n",
    "            delta_e += 2\n",
    "            delta_se += 2\n",
    "        else:\n",
    "            d += delta_se\n",
    "            delta_e += 2\n",
    "            delta_se += 4\n",
    "            y -= 1\n",
    "        \n",
    "        x += 1\n",
    "    \n",
    "    return points\n",
    "\n",
    "# Test the algorithm\n",
    "radius = 5\n",
    "\n",
    "# Midpoint circle drawing algorithm\n",
    "circle_points = draw_circle(radius)\n",
    "print(\"Circle Points:\", circle_points)\n",
    "\n",
    "# Plotting the circle\n",
    "plt.plot(*zip(*circle_points), marker='o')\n",
    "plt.axis('equal')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "632f36ce",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Clipped Line: (1, 1) (10, 8)\n"
     ]
    },
    {
     "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": [
    "#3\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Define the region codes\n",
    "INSIDE = 0  # 0000\n",
    "LEFT = 1    # 0001\n",
    "RIGHT = 2   # 0010\n",
    "BOTTOM = 4  # 0100\n",
    "TOP = 8     # 1000\n",
    "\n",
    "# Define the window boundaries\n",
    "x_min, y_min = 0, 0\n",
    "x_max, y_max = 10, 8\n",
    "\n",
    "def compute_region_code(x, y):\n",
    "    code = INSIDE\n",
    "    \n",
    "    if x < x_min:\n",
    "        code |= LEFT\n",
    "    elif x > x_max:\n",
    "        code |= RIGHT\n",
    "        \n",
    "    if y < y_min:\n",
    "        code |= BOTTOM\n",
    "    elif y > y_max:\n",
    "        code |= TOP\n",
    "    \n",
    "    return code\n",
    "\n",
    "def clip_line(x1, y1, x2, y2):\n",
    "    code1 = compute_region_code(x1, y1)\n",
    "    code2 = compute_region_code(x2, y2)\n",
    "    \n",
    "    while True:\n",
    "        if code1 == 0 and code2 == 0:\n",
    "            return x1, y1, x2, y2\n",
    "        \n",
    "        if code1 & code2 != 0:\n",
    "            return None\n",
    "        \n",
    "        code_out = code1 if code1 != 0 else code2\n",
    "        \n",
    "        x, y = None, None\n",
    "        \n",
    "        if code_out & TOP:\n",
    "            x = x1 + (x2 - x1) * (y_max - y1) / (y2 - y1)\n",
    "            y = y_max\n",
    "        elif code_out & BOTTOM:\n",
    "            x = x1 + (x2 - x1) * (y_min - y1) / (y2 - y1)\n",
    "            y = y_min\n",
    "        elif code_out & RIGHT:\n",
    "            y = y1 + (y2 - y1) * (x_max - x1) / (x2 - x1)\n",
    "            x = x_max\n",
    "        elif code_out & LEFT:\n",
    "            y = y1 + (y2 - y1) * (x_min - x1) / (x2 - x1)\n",
    "            x = x_min\n",
    "        \n",
    "        if code_out == code1:\n",
    "            x1, y1 = x, y\n",
    "            code1 = compute_region_code(x1, y1)\n",
    "        else:\n",
    "            x2, y2 = x, y\n",
    "            code2 = compute_region_code(x2, y2)\n",
    "\n",
    "# Test the algorithm\n",
    "x1, y1 = 1, 1\n",
    "x2, y2 = 10, 8\n",
    "\n",
    "# Clip the line using Cohen-Sutherland algorithm\n",
    "clipped_line = clip_line(x1, y1, x2, y2)\n",
    "if clipped_line is None:\n",
    "    print(\"Line is completely outside the window.\")\n",
    "else:\n",
    "    x1, y1, x2, y2 = clipped_line\n",
    "    print(\"Clipped Line:\", (x1, y1), (x2, y2))\n",
    "\n",
    "# Plotting the line and window\n",
    "plt.plot([x1, x2], [y1, y2], marker='o', label='Original Line')\n",
    "plt.plot([x_min, x_min, x_max, x_max, x_min], [y_min, y_max, y_max, y_min, y_min], 'r--', label='Window')\n",
    "plt.legend()\n",
    "plt.xlim(-2, 12)\n",
    "plt.ylim(-2, 10)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "352f337c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Clipped Polygon: [(6.0, 4), (3, 6), (3.0, 4)]\n"
     ]
    },
    {
     "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": [
    "#4\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Define the polygon vertices\n",
    "polygon = [(2, 1), (6, 1), (7, 4), (5, 7), (3, 6), (1, 4)]\n",
    "\n",
    "# Define the clipping window boundaries\n",
    "x_min, y_min = 3, 3\n",
    "x_max, y_max = 6, 6\n",
    "\n",
    "def inside(point):\n",
    "    x, y = point\n",
    "    return x_min <= x <= x_max and y_min <= y <= y_max\n",
    "\n",
    "def intersection(p1, p2, edge):\n",
    "    x1, y1 = p1\n",
    "    x2, y2 = p2\n",
    "    x_edge, y_edge = edge\n",
    "    \n",
    "    if y1 == y2:\n",
    "        x_int = x1\n",
    "        y_int = y_edge\n",
    "    else:\n",
    "        m_edge = (y_edge - y1) / (x_edge - x1)\n",
    "        b_edge = y_edge - m_edge * x_edge\n",
    "        \n",
    "        if m_edge == 0:\n",
    "            x_int = x_edge\n",
    "        else:\n",
    "            x_int = (y1 - b_edge) / m_edge\n",
    "        \n",
    "        y_int = y_edge\n",
    "    \n",
    "    return x_int, y_int\n",
    "\n",
    "\n",
    "def clip_polygon(polygon):\n",
    "    output_polygon = polygon\n",
    "    \n",
    "    for edge_start, edge_end in zip(polygon, polygon[1:] + [polygon[0]]):\n",
    "        input_polygon = output_polygon\n",
    "        output_polygon = []\n",
    "        \n",
    "        s = input_polygon[-1]\n",
    "        \n",
    "        for p in input_polygon:\n",
    "            if inside(p):\n",
    "                if not inside(s):\n",
    "                    output_polygon.append(intersection(s, p, edge_start))\n",
    "                output_polygon.append(p)\n",
    "            elif inside(s):\n",
    "                output_polygon.append(intersection(s, p, edge_start))\n",
    "            \n",
    "            s = p\n",
    "        \n",
    "    return output_polygon\n",
    "\n",
    "# Test the algorithm\n",
    "clipped_polygon = clip_polygon(polygon)\n",
    "print(\"Clipped Polygon:\", clipped_polygon)\n",
    "\n",
    "# Plotting the polygon and window\n",
    "x_poly, y_poly = zip(*polygon)\n",
    "x_clip, y_clip = zip(*clipped_polygon)\n",
    "\n",
    "plt.plot(x_poly, y_poly, marker='o', label='Original Polygon')\n",
    "plt.plot(x_clip, y_clip, marker='o', label='Clipped Polygon')\n",
    "plt.plot([x_min, x_min, x_max, x_max, x_min], [y_min, y_max, y_max, y_min, y_min], 'r--', label='Clipping Window')\n",
    "plt.legend()\n",
    "plt.xlim(0, 8)\n",
    "plt.ylim(0, 8)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "fe2534e2",
   "metadata": {
    "scrolled": false
   },
   "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"
    }
   ],
   "source": [
    "#5\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "# Define the polygon vertices\n",
    "polygon = [(1, 1), (4, 6), (7, 3), (4, 1)]\n",
    "\n",
    "def scan_line_fill(polygon):\n",
    "    # Find the minimum and maximum y-coordinate values\n",
    "    y_min = min(vertex[1] for vertex in polygon)\n",
    "    y_max = max(vertex[1] for vertex in polygon)\n",
    "\n",
    "    # Create an array to store the active edge table\n",
    "    aet = [[] for _ in range(y_min, y_max + 1)]\n",
    "\n",
    "    # Create an array to store the x-coordinates of the intersections\n",
    "    x_intersections = []\n",
    "\n",
    "    # Construct the active edge table\n",
    "    for i in range(len(polygon)):\n",
    "        x1, y1 = polygon[i]\n",
    "        x2, y2 = polygon[(i + 1) % len(polygon)]\n",
    "\n",
    "        # Ignore horizontal edges\n",
    "        if y1 != y2:\n",
    "            # Sort the endpoints by their y-coordinate\n",
    "            if y1 < y2:\n",
    "                y_start, x_start = y1, x1\n",
    "                y_end, x_end = y2, x2\n",
    "            else:\n",
    "                y_start, x_start = y2, x2\n",
    "                y_end, x_end = y1, x1\n",
    "\n",
    "            # Calculate the inverse slope of the edge\n",
    "            slope_inverse = (x_end - x_start) / (y_end - y_start)\n",
    "\n",
    "            # Add the edge to the active edge table at its starting y-coordinate\n",
    "            aet[y_start - y_min].append([x_start, slope_inverse])\n",
    "\n",
    "    # Fill the polygon using the scan line algorithm\n",
    "    for scan_line in range(y_min, y_max + 1):\n",
    "        # Add the x-coordinates of the edge intersections to the intersection array\n",
    "        for edge in aet[scan_line - y_min]:\n",
    "            x_intersections.append(edge[0])\n",
    "\n",
    "        # Sort the x-coordinates in ascending order\n",
    "        x_intersections.sort()\n",
    "\n",
    "        # Fill the pixels between each pair of intersections\n",
    "        for i in range(0, len(x_intersections), 2):\n",
    "            x_start = int(x_intersections[i])\n",
    "            x_end = int(x_intersections[i + 1]) if i + 1 < len(x_intersections) else x_start\n",
    "\n",
    "            plt.plot(range(x_start, x_end + 1), [scan_line] * (x_end - x_start + 1), color='black')\n",
    "\n",
    "        # Clear the intersection array for the next scan line\n",
    "        x_intersections.clear()\n",
    "\n",
    "        # Update the active edge table for the next scan line\n",
    "        for edge_list in aet:\n",
    "            for edge in edge_list:\n",
    "                edge[0] += edge[1]\n",
    "\n",
    "    plt.gca().invert_yaxis()\n",
    "    plt.axis('scaled')\n",
    "    plt.show()\n",
    "\n",
    "# Test the algorithm\n",
    "scan_line_fill(polygon)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "3b2f1519",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 5 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#6\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Define the object vertices\n",
    "object_vertices = np.array([\n",
    "    [1, 1],\n",
    "    [1, 3],\n",
    "    [3, 3],\n",
    "    [3, 1]\n",
    "])\n",
    "\n",
    "# Define the transformation matrices\n",
    "translation_matrix = np.array([\n",
    "    [1, 0, 2],\n",
    "    [0, 1, 2],\n",
    "    [0, 0, 1]\n",
    "])\n",
    "\n",
    "rotation_angle = np.pi / 4\n",
    "rotation_matrix = np.array([\n",
    "    [np.cos(rotation_angle), -np.sin(rotation_angle)],\n",
    "    [np.sin(rotation_angle), np.cos(rotation_angle)]\n",
    "])\n",
    "\n",
    "scaling_matrix = np.array([\n",
    "    [2, 0],\n",
    "    [0, 2]\n",
    "])\n",
    "\n",
    "# Apply the transformations\n",
    "translated_vertices = np.matmul(translation_matrix[:2, :2], object_vertices.T).T + translation_matrix[:2, 2]\n",
    "rotated_vertices = np.matmul(rotation_matrix, translated_vertices.T).T\n",
    "scaled_vertices = np.matmul(scaling_matrix, rotated_vertices.T).T\n",
    "\n",
    "# Plot the original and transformed objects\n",
    "plt.figure(figsize=(12, 4))\n",
    "\n",
    "# Plot the original object\n",
    "plt.subplot(2, 3, 1)\n",
    "plt.plot(object_vertices[:, 0], object_vertices[:, 1], 'b-')\n",
    "plt.title('Original Object')\n",
    "plt.axis('equal')\n",
    "\n",
    "# Plot the translated object\n",
    "plt.subplot(2, 3, 2)\n",
    "plt.plot(translated_vertices[:, 0], translated_vertices[:, 1], 'r-')\n",
    "plt.title('Translated Object')\n",
    "plt.axis('equal')\n",
    "\n",
    "# Plot the rotated object\n",
    "plt.subplot(2, 3, 3)\n",
    "plt.plot(rotated_vertices[:, 0], rotated_vertices[:, 1], 'g-')\n",
    "plt.title('Rotated Object')\n",
    "plt.axis('equal')\n",
    "\n",
    "# Plot the scaled object\n",
    "plt.subplot(2, 3, 4)\n",
    "plt.plot(scaled_vertices[:, 0], scaled_vertices[:, 1], 'm-')\n",
    "plt.title('Scaled Object')\n",
    "plt.axis('equal')\n",
    "\n",
    "# Plot the transformed object\n",
    "plt.subplot(2, 3, 5)\n",
    "plt.plot(transformed_vertices[:, 0], transformed_vertices[:, 1], 'r-')\n",
    "plt.title('Transformed Object')\n",
    "plt.axis('equal')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "77bf99d2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#7\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "\n",
    "# Define the 3D object\n",
    "object_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",
    "# Define the transformation matrices\n",
    "translation_matrix = np.array([\n",
    "    [1, 0, 0, 2],\n",
    "    [0, 1, 0, 2],\n",
    "    [0, 0, 1, 2],\n",
    "    [0, 0, 0, 1]\n",
    "])\n",
    "\n",
    "rotation_matrix = np.array([\n",
    "    [np.cos(np.pi/4), -np.sin(np.pi/4), 0, 0],\n",
    "    [np.sin(np.pi/4), np.cos(np.pi/4), 0, 0],\n",
    "    [0, 0, 1, 0],\n",
    "    [0, 0, 0, 1]\n",
    "])\n",
    "\n",
    "scaling_matrix = np.array([\n",
    "    [2, 0, 0, 0],\n",
    "    [0, 2, 0, 0],\n",
    "    [0, 0, 2, 0],\n",
    "    [0, 0, 0, 1]\n",
    "])\n",
    "\n",
    "# Apply the transformations\n",
    "homogeneous_vertices = np.hstack((object_vertices, np.ones((object_vertices.shape[0], 1))))\n",
    "translated_vertices = np.matmul(translation_matrix, homogeneous_vertices.T).T\n",
    "rotated_vertices = np.matmul(rotation_matrix, translated_vertices.T).T\n",
    "transformed_vertices = np.matmul(scaling_matrix, rotated_vertices.T).T\n",
    "\n",
    "# Perform parallel projection\n",
    "parallel_projection_matrix = np.array([\n",
    "    [1, 0, 0, 0],\n",
    "    [0, 1, 0, 0],\n",
    "    [0, 0, 0, 0],\n",
    "    [0, 0, 0, 1]\n",
    "])\n",
    "\n",
    "parallel_projected_vertices = np.matmul(parallel_projection_matrix, transformed_vertices.T).T\n",
    "\n",
    "# Perform perspective projection\n",
    "perspective_projection_matrix = np.array([\n",
    "    [1, 0, 0, 0],\n",
    "    [0, 1, 0, 0],\n",
    "    [0, 0, 0, 1/4],\n",
    "    [0, 0, 0, 0]\n",
    "])\n",
    "\n",
    "perspective_projected_vertices = np.matmul(perspective_projection_matrix, transformed_vertices.T).T\n",
    "\n",
    "# Plot the 3D object and projections\n",
    "fig = plt.figure(figsize=(12, 6))\n",
    "\n",
    "# Plot the original 3D object\n",
    "ax1 = fig.add_subplot(131, projection='3d')\n",
    "ax1.scatter(object_vertices[:, 0], object_vertices[:, 1], object_vertices[:, 2])\n",
    "ax1.set_title('Original 3D Object')\n",
    "\n",
    "# Plot the parallel projection\n",
    "ax2 = fig.add_subplot(132)\n",
    "ax2.scatter(parallel_projected_vertices[:, 0], parallel_projected_vertices[:, 1])\n",
    "ax2.set_title('Parallel Projection')\n",
    "\n",
    "# Plot the perspective projection\n",
    "ax3 = fig.add_subplot(133)\n",
    "ax3.scatter(perspective_projected_vertices[:, 0], perspective_projected_vertices[:, 1])\n",
    "ax3.set_title('Perspective Projection')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "3667f84e",
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "The shapes of `y` and `dydx` must be identical.",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "Input \u001b[1;32mIn [42]\u001b[0m, in \u001b[0;36m<cell line: 19>\u001b[1;34m()\u001b[0m\n\u001b[0;32m     16\u001b[0m tangents \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39marray([[\u001b[38;5;241m1\u001b[39m, \u001b[38;5;241m0.5\u001b[39m], [\u001b[38;5;241m1\u001b[39m, \u001b[38;5;241m-\u001b[39m\u001b[38;5;241m1\u001b[39m]])\n\u001b[0;32m     18\u001b[0m \u001b[38;5;66;03m# Generate the Hermite curve\u001b[39;00m\n\u001b[1;32m---> 19\u001b[0m hermite_points \u001b[38;5;241m=\u001b[39m \u001b[43mhermite_curve\u001b[49m\u001b[43m(\u001b[49m\u001b[43mpoints\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mtangents\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m     21\u001b[0m \u001b[38;5;66;03m# Plot the Hermite curve\u001b[39;00m\n\u001b[0;32m     22\u001b[0m plt\u001b[38;5;241m.\u001b[39mplot(hermite_points[:, \u001b[38;5;241m0\u001b[39m], hermite_points[:, \u001b[38;5;241m1\u001b[39m])\n",
      "Input \u001b[1;32mIn [42]\u001b[0m, in \u001b[0;36mhermite_curve\u001b[1;34m(points, tangents, num_points)\u001b[0m\n\u001b[0;32m      6\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[0;32m      7\u001b[0m \u001b[38;5;124;03mGenerate a Hermite curve given the points and tangents at each point.\u001b[39;00m\n\u001b[0;32m      8\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[0;32m      9\u001b[0m t \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mlinspace(\u001b[38;5;241m0\u001b[39m, \u001b[38;5;241m1\u001b[39m, \u001b[38;5;28mlen\u001b[39m(points))\n\u001b[1;32m---> 10\u001b[0m spline \u001b[38;5;241m=\u001b[39m \u001b[43mCubicHermiteSpline\u001b[49m\u001b[43m(\u001b[49m\u001b[43mt\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mpoints\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mT\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mtangents\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mT\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m     11\u001b[0m t_new \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mlinspace(\u001b[38;5;241m0\u001b[39m, \u001b[38;5;241m1\u001b[39m, num_points)\n\u001b[0;32m     12\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m spline(t_new)\u001b[38;5;241m.\u001b[39mT\n",
      "File \u001b[1;32mc:\\python39\\lib\\site-packages\\scipy\\interpolate\\_cubic.py:140\u001b[0m, in \u001b[0;36mCubicHermiteSpline.__init__\u001b[1;34m(self, x, y, dydx, axis, extrapolate)\u001b[0m\n\u001b[0;32m    137\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m extrapolate \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[0;32m    138\u001b[0m     extrapolate \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mTrue\u001b[39;00m\n\u001b[1;32m--> 140\u001b[0m x, dx, y, axis, dydx \u001b[38;5;241m=\u001b[39m \u001b[43mprepare_input\u001b[49m\u001b[43m(\u001b[49m\u001b[43mx\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43my\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43maxis\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdydx\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m    142\u001b[0m dxr \u001b[38;5;241m=\u001b[39m dx\u001b[38;5;241m.\u001b[39mreshape([dx\u001b[38;5;241m.\u001b[39mshape[\u001b[38;5;241m0\u001b[39m]] \u001b[38;5;241m+\u001b[39m [\u001b[38;5;241m1\u001b[39m] \u001b[38;5;241m*\u001b[39m (y\u001b[38;5;241m.\u001b[39mndim \u001b[38;5;241m-\u001b[39m \u001b[38;5;241m1\u001b[39m))\n\u001b[0;32m    143\u001b[0m slope \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mdiff(y, axis\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m0\u001b[39m) \u001b[38;5;241m/\u001b[39m dxr\n",
      "File \u001b[1;32mc:\\python39\\lib\\site-packages\\scipy\\interpolate\\_cubic.py:36\u001b[0m, in \u001b[0;36mprepare_input\u001b[1;34m(x, y, axis, dydx)\u001b[0m\n\u001b[0;32m     34\u001b[0m dydx \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39masarray(dydx)\n\u001b[0;32m     35\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m y\u001b[38;5;241m.\u001b[39mshape \u001b[38;5;241m!=\u001b[39m dydx\u001b[38;5;241m.\u001b[39mshape:\n\u001b[1;32m---> 36\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mThe shapes of `y` and `dydx` must be identical.\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[0;32m     37\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m np\u001b[38;5;241m.\u001b[39missubdtype(dydx\u001b[38;5;241m.\u001b[39mdtype, np\u001b[38;5;241m.\u001b[39mcomplexfloating):\n\u001b[0;32m     38\u001b[0m     dtype \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mcomplex\u001b[39m\n",
      "\u001b[1;31mValueError\u001b[0m: The shapes of `y` and `dydx` must be identical."
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.interpolate import CubicHermiteSpline\n",
    "\n",
    "def hermite_curve(points, tangents, num_points=100):\n",
    "    \"\"\"\n",
    "    Generate a Hermite curve given the points and tangents at each point.\n",
    "    \"\"\"\n",
    "    t = np.linspace(0, 1, len(points))\n",
    "    spline = CubicHermiteSpline(t, points.T, tangents.T)\n",
    "    t_new = np.linspace(0, 1, num_points)\n",
    "    return spline(t_new).T\n",
    "\n",
    "# Define the points and tangents for the Hermite curve\n",
    "points = np.array([[0, 0], [1, 1], [2, -1], [3, 0]])\n",
    "tangents = np.array([[1, 0.5], [1, -1]])\n",
    "\n",
    "# Generate the Hermite curve\n",
    "hermite_points = hermite_curve(points, tangents)\n",
    "\n",
    "# Plot the Hermite curve\n",
    "plt.plot(hermite_points[:, 0], hermite_points[:, 1])\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e277a484",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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