main.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ray Tracing from  base in Python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from tqdm import tqdm\n",
    "\n",
    "width = 300\n",
    "height = 200"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Defining the objects and light sources"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the objects present in the scene\n",
    "objects = [\n",
    "    {\n",
    "        \"center\": np.array([-0.2, 0, -1]),\n",
    "        \"radius\": 0.7,\n",
    "        \"ambient\": np.array([0.1, 0, 0]),\n",
    "        \"diffuse\": np.array([0.7, 0, 0]),\n",
    "        \"specular\": np.array([1, 1, 1]),\n",
    "        \"shininess\": 100,\n",
    "    },\n",
    "    {\n",
    "        \"center\": np.array([0.1, -0.3, 0]),\n",
    "        \"radius\": 0.1,\n",
    "        \"ambient\": np.array([0.1, 0, 0.1]),\n",
    "        \"diffuse\": np.array([0.7, 0, 0.7]),\n",
    "        \"specular\": np.array([1, 1, 1]),\n",
    "        \"shininess\": 100,\n",
    "    },\n",
    "    {\n",
    "        \"center\": np.array([-0.3, 0, 0]),\n",
    "        \"radius\": 0.15,\n",
    "        \"ambient\": np.array([0, 0.1, 0]),\n",
    "        \"diffuse\": np.array([0, 0.6, 0]),\n",
    "        \"specular\": np.array([1, 1, 1]),\n",
    "        \"shininess\": 100,\n",
    "    },\n",
    "]\n",
    "# Define the light source\n",
    "light = {\n",
    "    \"position\": np.array([5, 5, 5]),\n",
    "    \"ambient\": np.array([1, 1, 1]),\n",
    "    \"diffuse\": np.array([1, 1, 1]),\n",
    "    \"specular\": np.array([1, 1, 1]),\n",
    "}\n",
    "\n",
    "camera = np.array([0, 0, 1])\n",
    "ratio = 1.0 * width / height\n",
    "screen = (-1, 1.0 / ratio, 1, -1.0 / ratio)  # left, top, right, bottom"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Do the ray tracing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_sphere_intersect(sphere_center, sphere_radius, ray_origin, ray_direction):\n",
    "    \"\"\"\n",
    "    Return the closest intersection point between the ray and the sphere\n",
    "    \"\"\"\n",
    "    a = np.linalg.norm(ray_direction) ** 2  # if normalized, this is 1\n",
    "    b = 2 * np.dot(ray_direction, ray_origin - sphere_center)\n",
    "    c = np.linalg.norm(ray_origin - sphere_center) ** 2 - sphere_radius**2\n",
    "    delta = b**2 - 4 * a * c\n",
    "\n",
    "    if delta > 0:\n",
    "        t1 = (-b - np.sqrt(delta)) / (2 * a)\n",
    "        t2 = (-b + np.sqrt(delta)) / (2 * a)\n",
    "\n",
    "        if t1 > 0 and t2 > 0:  # check if the intersection is in front of the camera\n",
    "            return min(t1, t2)  # return the closest intersection point\n",
    "\n",
    "    return None\n",
    "\n",
    "\n",
    "def nearest_intersected_object(objects, ray_origin, ray_direction):\n",
    "    \"\"\"\n",
    "    Return the nearest object and its intersection point with the ray\n",
    "    \"\"\"\n",
    "    distances = [\n",
    "        get_sphere_intersect(obj[\"center\"], obj[\"radius\"], ray_origin, ray_direction)\n",
    "        for obj in objects\n",
    "    ]\n",
    "    nearest_object = None\n",
    "    min_distance = np.inf\n",
    "\n",
    "    for index, distance in enumerate(distances):\n",
    "        if distance and distance < min_distance:\n",
    "            min_distance = distance\n",
    "            nearest_object = objects[index]\n",
    "\n",
    "    return nearest_object, min_distance\n",
    "\n",
    "\n",
    "def ray_tracing():\n",
    "    image = np.zeros((height, width, 3))\n",
    "\n",
    "    for i, y in tqdm(enumerate(np.linspace(screen[1], screen[3], height))):\n",
    "        for j, x in enumerate(np.linspace(screen[0], screen[2], width)):\n",
    "            pixel = np.array([x, y, 0])\n",
    "            direction = pixel - camera\n",
    "            direction /= np.linalg.norm(direction)  # normalize\n",
    "\n",
    "            # Find the nearest intersection\n",
    "            nearest_object, min_distance = nearest_intersected_object(\n",
    "                objects, camera, direction\n",
    "            )\n",
    "\n",
    "            if nearest_object is None:\n",
    "                continue\n",
    "\n",
    "            intersection = camera + min_distance * direction\n",
    "\n",
    "            # find the normal to the intersection point\n",
    "            normal_to_surface = intersection - nearest_object[\"center\"]\n",
    "            normal_to_surface /= np.linalg.norm(normal_to_surface)  # normalize\n",
    "\n",
    "            # find the unit direction vector from the intersection point to the light source\n",
    "            light_direction = light[\"position\"] - intersection\n",
    "            light_direction /= np.linalg.norm(light_direction)  # normalize\n",
    "\n",
    "            _, min_distance = nearest_intersected_object(\n",
    "                objects, intersection, light_direction\n",
    "            )\n",
    "            intersect_to_light_dist = np.linalg.norm(light[\"position\"] - intersection)\n",
    "            is_shadowed = min_distance < intersect_to_light_dist\n",
    "\n",
    "            if is_shadowed:\n",
    "                continue\n",
    "\n",
    "            # RGB using Blenn-Phong model\n",
    "            illumination = np.zeros((3))\n",
    "\n",
    "            # add ambient\n",
    "            illumination += nearest_object[\"ambient\"] * light[\"ambient\"]\n",
    "\n",
    "            # add diffuse\n",
    "            illumination += (\n",
    "                nearest_object[\"diffuse\"]\n",
    "                * light[\"diffuse\"]\n",
    "                * np.dot(light_direction, normal_to_surface)\n",
    "            )\n",
    "\n",
    "            # add specular\n",
    "            intersect_to_camera = camera - intersection\n",
    "            intersect_to_camera /= np.linalg.norm(intersect_to_camera)  # normalize\n",
    "\n",
    "            H = intersect_to_camera + light_direction\n",
    "            H /= np.linalg.norm(H)  # normalize\n",
    "\n",
    "            illumination += (\n",
    "                nearest_object[\"specular\"]\n",
    "                * light[\"specular\"]\n",
    "                * np.dot(normal_to_surface, H) ** (nearest_object[\"shininess\"] / 4)\n",
    "            )\n",
    "\n",
    "            # set the pixel color\n",
    "            image[i, j] = np.clip(illumination, 0, 1)\n",
    "\n",
    "    plt.imshow(image)\n",
    "    plt.show()\n",
    "    return image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "200it [00:01, 142.28it/s]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "image = ray_tracing()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualize the environment in 3D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%pip install plotly nbformat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "plotlyServerURL": "https://plot.ly"
       },
       "data": [
        {
         "marker": {
          "color": "lightpink",
          "size": 35
         },
         "mode": "markers",
         "name": "sphere",
         "type": "scatter3d",
         "x": [
          -0.2
         ],
         "y": [
          0
         ],
         "z": [
          -1
         ]
        },
        {
         "marker": {
          "color": "lightpink",
          "size": 5
         },
         "mode": "markers",
         "name": "sphere",
         "type": "scatter3d",
         "x": [
          0.1
         ],
         "y": [
          -0.3
         ],
         "z": [
          0
         ]
        },
        {
         "marker": {
          "color": "lightpink",
          "size": 7.5
         },
         "mode": "markers",
         "name": "sphere",
         "type": "scatter3d",
         "x": [
          -0.3
         ],
         "y": [
          0
         ],
         "z": [
          0
         ]
        },
        {
         "color": "gray",
         "name": "image plane",
         "opacity": 0.5,
         "type": "mesh3d",
         "x": [
          -1,
          -1,
          1,
          1
         ],
         "y": [
          0.6666666666666666,
          -0.6666666666666666,
          0.6666666666666666,
          -0.6666666666666666
         ],
         "z": [
          0,
          0,
          0,
          0
         ]
        },
        {
         "marker": {
          "color": "yellow",
          "size": 10
         },
         "mode": "markers",
         "name": "light source",
         "type": "scatter3d",
         "x": [
          5
         ],
         "y": [
          5
         ],
         "z": [
          5
         ]
        }
       ],
       "layout": {
        "scene": {
         "camera": {
          "eye": {
           "x": 0,
           "y": 0,
           "z": 1
          }
         }
        },
        "template": {
         "data": {
          "bar": [
           {
            "error_x": {
             "color": "#2a3f5f"
            },
            "error_y": {
             "color": "#2a3f5f"
            },
            "marker": {
             "line": {
              "color": "#E5ECF6",
              "width": 0.5
             },
             "pattern": {
              "fillmode": "overlay",
              "size": 10,
              "solidity": 0.2
             }
            },
            "type": "bar"
           }
          ],
          "barpolar": [
           {
            "marker": {
             "line": {
              "color": "#E5ECF6",
              "width": 0.5
             },
             "pattern": {
              "fillmode": "overlay",
              "size": 10,
              "solidity": 0.2
             }
            },
            "type": "barpolar"
           }
          ],
          "carpet": [
           {
            "aaxis": {
             "endlinecolor": "#2a3f5f",
             "gridcolor": "white",
             "linecolor": "white",
             "minorgridcolor": "white",
             "startlinecolor": "#2a3f5f"
            },
            "baxis": {
             "endlinecolor": "#2a3f5f",
             "gridcolor": "white",
             "linecolor": "white",
             "minorgridcolor": "white",
             "startlinecolor": "#2a3f5f"
            },
            "type": "carpet"
           }
          ],
          "choropleth": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "choropleth"
           }
          ],
          "contour": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "contour"
           }
          ],
          "contourcarpet": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "contourcarpet"
           }
          ],
          "heatmap": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "heatmap"
           }
          ],
          "heatmapgl": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "heatmapgl"
           }
          ],
          "histogram": [
           {
            "marker": {
             "pattern": {
              "fillmode": "overlay",
              "size": 10,
              "solidity": 0.2
             }
            },
            "type": "histogram"
           }
          ],
          "histogram2d": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "histogram2d"
           }
          ],
          "histogram2dcontour": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "histogram2dcontour"
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             "outlinewidth": 0,
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            "type": "mesh3d"
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            },
            "type": "parcoords"
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           {
            "automargin": true,
            "type": "pie"
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          ],
          "scatter": [
           {
            "fillpattern": {
             "fillmode": "overlay",
             "size": 10,
             "solidity": 0.2
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            "type": "scatter"
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            "type": "scattercarpet"
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            "type": "scattergeo"
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            "type": "scattergl"
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              "outlinewidth": 0,
              "ticks": ""
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            },
            "type": "scattermapbox"
           }
          ],
          "scatterpolar": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
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            },
            "type": "scatterpolar"
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          ],
          "scatterpolargl": [
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             "colorbar": {
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            "type": "scatterpolargl"
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          "scatterternary": [
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             "colorbar": {
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              "ticks": ""
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            "type": "scatterternary"
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          ],
          "surface": [
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            "type": "surface"
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          "table": [
           {
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              "color": "#EBF0F8"
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             "line": {
              "color": "white"
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            },
            "header": {
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             "line": {
              "color": "white"
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         "layout": {
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          "font": {
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          },
          "geo": {
           "bgcolor": "white",
           "lakecolor": "white",
           "landcolor": "#E5ECF6",
           "showlakes": true,
           "showland": true,
           "subunitcolor": "white"
          },
          "hoverlabel": {
           "align": "left"
          },
          "hovermode": "closest",
          "mapbox": {
           "style": "light"
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          "plot_bgcolor": "#E5ECF6",
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           },
           "bgcolor": "#E5ECF6",
           "radialaxis": {
            "gridcolor": "white",
            "linecolor": "white",
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          },
          "scene": {
           "xaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
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           "yaxis": {
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            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
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           "zaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           }
          },
          "shapedefaults": {
           "line": {
            "color": "#2a3f5f"
           }
          },
          "ternary": {
           "aaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "baxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "caxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "title": {
           "x": 0.05
          },
          "xaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          },
          "yaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          }
         }
        }
       }
      }
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import plotly.graph_objects as go\n",
    "\n",
    "fig = go.Figure()\n",
    "\n",
    "# set the main camera at the camera_origin\n",
    "fig.update_layout(scene_camera_eye=dict(x=camera[0], y=camera[1], z=camera[2]))\n",
    "\n",
    "# Show the objects\n",
    "for obj in objects:\n",
    "    fig.add_trace(\n",
    "        # Plot the sphere\n",
    "        go.Scatter3d(\n",
    "            x=[obj[\"center\"][0]],\n",
    "            y=[obj[\"center\"][1]],\n",
    "            z=[obj[\"center\"][2]],\n",
    "            mode=\"markers\",\n",
    "            marker=dict(color=\"lightpink\", size=obj[\"radius\"] * 50),\n",
    "            name=\"sphere\",\n",
    "        )\n",
    "    )\n",
    "\n",
    "# Show the image screen as a plane with low opacity\n",
    "fig.add_trace(\n",
    "    go.Mesh3d(\n",
    "        x=[screen[0], screen[0], screen[2], screen[2]],\n",
    "        y=[screen[1], screen[3], screen[1], screen[3]],\n",
    "        z=[0, 0, 0, 0],\n",
    "        opacity=0.5,\n",
    "        color=\"gray\",\n",
    "        name=\"image plane\",\n",
    "    )\n",
    ")\n",
    "\n",
    "# Show the light source as a yellow sphere\n",
    "fig.add_trace(\n",
    "    go.Scatter3d(\n",
    "        x=[light[\"position\"][0]],\n",
    "        y=[light[\"position\"][1]],\n",
    "        z=[light[\"position\"][2]],\n",
    "        mode=\"markers\",\n",
    "        marker=dict(color=\"yellow\", size=10),\n",
    "        name=\"light source\",\n",
    "    )\n",
    ")\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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