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KleinBottle0.ipynb
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| "id": "GxJ8MecbqoSa", | |
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| ] | |
| }, | |
| "metadata": {} | |
| }, | |
| { | |
| "output_type": "error", | |
| "ename": "ValueError", | |
| "evalue": "\nImage export using the \"kaleido\" engine requires the kaleido package,\nwhich can be installed using pip:\n $ pip install -U kaleido\n", | |
| "traceback": [ | |
| "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", | |
| "\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)", | |
| "\u001b[0;32m<ipython-input-2-fa40fb424629>\u001b[0m in \u001b[0;36m<cell line: 0>\u001b[0;34m()\u001b[0m\n\u001b[1;32m 40\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 41\u001b[0m \u001b[0;31m# Save the image\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 42\u001b[0;31m \u001b[0mfig\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mwrite_image\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"klein_bottle_plotly.png\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", | |
| "\u001b[0;32m/usr/local/lib/python3.11/dist-packages/plotly/basedatatypes.py\u001b[0m in \u001b[0;36mwrite_image\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m 3833\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mplotly\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mio\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mpio\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3834\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 3835\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mpio\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mwrite_image\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 3836\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3837\u001b[0m \u001b[0;31m# Static helpers\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", | |
| "\u001b[0;32m/usr/local/lib/python3.11/dist-packages/plotly/io/_kaleido.py\u001b[0m in \u001b[0;36mwrite_image\u001b[0;34m(fig, file, format, scale, width, height, validate, engine)\u001b[0m\n\u001b[1;32m 264\u001b[0m \u001b[0;31m# -------------\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 265\u001b[0m \u001b[0;31m# Do this first so we don't create a file if image conversion fails\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 266\u001b[0;31m img_data = to_image(\n\u001b[0m\u001b[1;32m 267\u001b[0m \u001b[0mfig\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 268\u001b[0m \u001b[0mformat\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mformat\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", | |
| "\u001b[0;32m/usr/local/lib/python3.11/dist-packages/plotly/io/_kaleido.py\u001b[0m in \u001b[0;36mto_image\u001b[0;34m(fig, format, width, height, scale, validate, engine)\u001b[0m\n\u001b[1;32m 130\u001b[0m \u001b[0;31m# Raise informative error message if Kaleido is not installed\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 131\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mscope\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 132\u001b[0;31m raise ValueError(\n\u001b[0m\u001b[1;32m 133\u001b[0m \"\"\"\n\u001b[1;32m 134\u001b[0m \u001b[0mImage\u001b[0m \u001b[0mexport\u001b[0m \u001b[0musing\u001b[0m \u001b[0mthe\u001b[0m \u001b[0;34m\"kaleido\"\u001b[0m \u001b[0mengine\u001b[0m \u001b[0mrequires\u001b[0m \u001b[0mthe\u001b[0m \u001b[0mkaleido\u001b[0m \u001b[0mpackage\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", | |
| "\u001b[0;31mValueError\u001b[0m: \nImage export using the \"kaleido\" engine requires the kaleido package,\nwhich can be installed using pip:\n $ pip install -U kaleido\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "import numpy as np\n", | |
| "import plotly.graph_objects as go\n", | |
| "\n", | |
| "# Parametric equations for the Klein bottle\n", | |
| "def klein_bottle(u, v):\n", | |
| " u = u * 2 * np.pi # u ranges from 0 to 2π\n", | |
| " v = v * 2 * np.pi # v ranges from 0 to 2π\n", | |
| " half = (0 <= u) & (u < np.pi)\n", | |
| " r = 4 * (1 - np.cos(u) / 2)\n", | |
| " x = np.zeros_like(u)\n", | |
| " y = np.zeros_like(u)\n", | |
| " z = np.zeros_like(u)\n", | |
| "\n", | |
| " x[half] = 6 * np.cos(u[half]) * (1 + np.sin(u[half])) + r[half] * np.cos(u[half]) * np.cos(v[half])\n", | |
| " y[half] = 16 * np.sin(u[half]) + r[half] * np.sin(u[half]) * np.cos(v[half])\n", | |
| " x[~half] = 6 * np.cos(u[~half]) * (1 + np.sin(u[~half])) + r[~half] * np.cos(v[~half] + np.pi)\n", | |
| " y[~half] = 16 * np.sin(u[~half])\n", | |
| " z = -r * np.sin(v)\n", | |
| "\n", | |
| " return x, y, z\n", | |
| "\n", | |
| "# Generate grid of u and v values\n", | |
| "u = np.linspace(0, 1, 100)\n", | |
| "v = np.linspace(0, 1, 100)\n", | |
| "u, v = np.meshgrid(u, v)\n", | |
| "\n", | |
| "# Compute the coordinates of the Klein bottle\n", | |
| "x, y, z = klein_bottle(u, v)\n", | |
| "\n", | |
| "# Create a 3D surface plot with Plotly\n", | |
| "fig = go.Figure(data=[go.Surface(z=z, x=x, y=y, colorscale='Viridis')])\n", | |
| "fig.update_layout(title=\"Klein Bottle\", scene=dict(\n", | |
| " xaxis_title='X',\n", | |
| " yaxis_title='Y',\n", | |
| " zaxis_title='Z'\n", | |
| "))\n", | |
| "\n", | |
| "# Show the interactive plot\n", | |
| "fig.show()\n", | |
| "\n", | |
| "# Save the image\n", | |
| "fig.write_image(\"klein_bottle_plotly.png\")" | |
| ] | |
| } | |
| ] | |
| } |
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