{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "WMYGesN_u0od"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from mpl_toolkits.mplot3d import Axes3D\n",
        "\n",
        "# Constants and functions\n",
        "r = 0.5  # Radius of the circle\n",
        "x0 = np.array([1, 1])  # Initial point\n",
        "\n",
        "def Y(l):\n",
        "    return np.array([np.cos(l), np.sin(l)])\n",
        "\n",
        "# Curves x(s,l)\n",
        "def x(s, l):\n",
        "    return x0 + r * np.sin(s) * Y(l)\n",
        "\n",
        "# Cone function\n",
        "# This function correctly now calculates a point on the cone based on s, l and t.\n",
        "def cone(s, l, t):\n",
        "    x_sl = x(s, l)\n",
        "    return np.array([np.cos(t) * x_sl[0], np.sin(t) * x_sl[1], t])\n",
        "\n",
        "# Parametric plot of the folded cone (corrected version)\n",
        "fig = plt.figure()\n",
        "ax = fig.add_subplot(111, projection='3d')\n",
        "\n",
        "# Creating the meshgrid properly using numpy\n",
        "s = np.linspace(0, np.pi/2, 50)  # s (parameter along the arc)\n",
        "l = np.linspace(0, 2*np.pi, 50)  # l (parameter around the circle)\n",
        "t = np.linspace(0, 1, 50)  # t (parameter along the cone height)\n",
        "\n",
        "# Using NumPy's broadcasting to compute the cone points - This avoids loops and is efficient.\n",
        "S, T = np.meshgrid(s, t)\n",
        "L = np.tile(l, (len(t), 1)).T  # This creates a repeated array of l for each t value.\n",
        "\n",
        "# Now we evaluate the cone function on the grid points.\n",
        "# We need to 'vectorize' our cone function for it to work on arrays.\n",
        "cone_pts = np.vectorize(cone, signature='(),(),()->(n)')(S, L, T)\n",
        "\n",
        "# We extract X, Y, Z coordinates for plotting\n",
        "X = cone_pts[..., 0]\n",
        "Y = cone_pts[..., 1]\n",
        "Z = cone_pts[..., 2]\n",
        "\n",
        "# Plot the surface. The surface is defined by the X, Y, Z arrays.\n",
        "ax.plot_surface(X, Y, Z, alpha=0.8, cmap='viridis')\n",
        "\n",
        "# Combining the plot with a base circle at the bottom.\n",
        "# We use the first row of X, Y since it corresponds to the base circle (t=0).\n",
        "ax.plot(X[0], Y[0], np.zeros_like(X[0]), color='red', linewidth=2)\n",
        "\n",
        "# Hide axes for better visibility\n",
        "plt.axis('off')\n",
        "\n",
        "# Show the plot\n",
        "plt.show()"
      ]
    }
  ]
}