{
 "cells": [
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-02-04T08:51:31.132029Z",
     "start_time": "2026-02-04T08:51:31.117737Z"
    }
   },
   "cell_type": "code",
   "source": [
    "import plotly.graph_objects as go\n",
    "import numpy as np\n",
    "from ellipsoide import EllipsoidTriaxial\n",
    "import winkelumrechnungen as wu"
   ],
   "id": "731173e4745cfe7c",
   "outputs": [],
   "execution_count": 17
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-02-04T08:51:31.167278Z",
     "start_time": "2026-02-04T08:51:31.146740Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def ellipsoid_figure(ell: EllipsoidTriaxial, title=\"Dreiachsiges Ellipsoid\", all=True, opac=1.0):\n",
    "    fig = go.Figure()\n",
    "\n",
    "    # Darstellung\n",
    "    rx, ry, rz = 1.3*ell.ax, 1.3*ell.ax, 1.3*ell.ax\n",
    "    fig.update_layout(\n",
    "        title=title,\n",
    "        scene=dict(\n",
    "            xaxis=dict(range=[-rx, rx], title=\"\"),\n",
    "            yaxis=dict(range=[-ry, ry], title=\"\"),\n",
    "            zaxis=dict(range=[-rz, rz], title=\"\"),\n",
    "            aspectmode=\"data\"\n",
    "        ),\n",
    "        margin=dict(l=0, r=0, t=10, b=0),\n",
    "    )\n",
    "    # Ellipsoid\n",
    "    if all:\n",
    "        u = np.linspace(-np.pi/2, np.pi/2, 181)\n",
    "        v = np.linspace(-np.pi,     np.pi,   181)\n",
    "    else:\n",
    "        u = np.linspace(0, np.pi/2, 91)\n",
    "        v = np.linspace(0,     np.pi/2,   91)\n",
    "\n",
    "    U, V = np.meshgrid(u, v)\n",
    "    X, Y, Z = ell.para2cart(U, V)\n",
    "    fig.add_trace(go.Surface(\n",
    "        x=X, y=Y, z=Z, showscale=False, opacity=opac,\n",
    "        surfacecolor=np.zeros_like(X),\n",
    "        colorscale=[[0, \"rgb(200,220,255)\"], [1, \"rgb(200,220,255)\"]],\n",
    "        name=\"Ellipsoid\", showlegend = True\n",
    "    ))\n",
    "\n",
    "    return fig"
   ],
   "id": "ea4aff9721cc92c0",
   "outputs": [],
   "execution_count": 18
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-02-04T08:51:31.194432Z",
     "start_time": "2026-02-04T08:51:31.180811Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def show_spere(fig, ell: EllipsoidTriaxial, all=True, opac=1.0):\n",
    "    # Darstellung\n",
    "    r = float(ell.ax)\n",
    "\n",
    "    # Parameterbereich\n",
    "    if all:\n",
    "        # ganze Kugel\n",
    "        u = np.linspace(-np.pi / 2, np.pi / 2, 181)  # Breite/Latitude\n",
    "        v = np.linspace(-np.pi, np.pi, 181)          # Länge/Longitude\n",
    "    else:\n",
    "        # nur Oktant (analog zu deinem Viertel-Setup)\n",
    "        u = np.linspace(0, np.pi / 2, 91)\n",
    "        v = np.linspace(0, np.pi / 2, 91)\n",
    "\n",
    "    U, V = np.meshgrid(u, v)\n",
    "\n",
    "    # Kugelparametrisierung (Latitude/Longitude)\n",
    "    X = r * np.cos(U) * np.cos(V)\n",
    "    Y = r * np.cos(U) * np.sin(V)\n",
    "    Z = r * np.sin(U)\n",
    "\n",
    "    fig.add_trace(go.Surface(\n",
    "        x=X, y=Y, z=Z, showscale=False, opacity=opac,\n",
    "        surfacecolor=np.zeros_like(X),\n",
    "        colorscale=[[0, \"rgb(255,180,180)\"], [1, \"rgb(255,180,180)\"]],\n",
    "        name=\"Kugel\", showlegend = True\n",
    "    ))\n",
    "\n",
    "    return fig"
   ],
   "id": "82255922e18e77e0",
   "outputs": [],
   "execution_count": 19
  },
  {
   "metadata": {
    "jupyter": {
     "is_executing": true
    },
    "ExecuteTime": {
     "start_time": "2026-02-04T10:52:53.553864Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def figure_constant_lines(fig, ell: EllipsoidTriaxial, coordsystem: str = \"para\", linewidth=1, color1=\"black\", color2=\"grey\"):\n",
    "    if coordsystem == \"para\":\n",
    "        constants_u = wu.deg2rad(np.arange(-90, 91, 15))\n",
    "        all_v = wu.deg2rad(np.arange(-180, 180, 0.5))\n",
    "        for u in constants_u:\n",
    "            xm, ym, zm = ell.para2cart(u, all_v)\n",
    "            fig.add_trace(go.Scatter3d(\n",
    "                x=xm, y=ym, z=zm, mode=\"lines\",\n",
    "                line=dict(width=linewidth, color=color1), name=\"constant u\",\n",
    "                showlegend=(True if u == constants_u[0] else False)\n",
    "            ))\n",
    "\n",
    "        all_u = wu.deg2rad(np.arange(-90, 91, 0.5))\n",
    "        constants_v = wu.deg2rad(np.arange(-180, 180, 15))\n",
    "        for v in constants_v:\n",
    "            x, y, z = ell.para2cart(all_u, v)\n",
    "            fig.add_trace(go.Scatter3d(\n",
    "                x=x, y=y, z=z, mode=\"lines\",\n",
    "                line=dict(width=linewidth, color=color2), name=\"constant v\",\n",
    "                showlegend=(True if v == constants_v[0] else False)\n",
    "            ))\n",
    "\n",
    "    elif coordsystem == \"ell\":\n",
    "        constants_beta = wu.deg2rad(np.arange(-90, 91, 15))\n",
    "        all_lamb = wu.deg2rad(np.arange(-180, 180, 0.5))\n",
    "        for beta in constants_beta:\n",
    "            xyz = ell.ell2cart(beta, all_lamb)\n",
    "            fig.add_trace(go.Scatter3d(\n",
    "                x=xyz[:, 0], y=xyz[:, 1], z=xyz[:, 2], mode=\"lines\", name=\"constant β\",\n",
    "                line=dict(width=linewidth, color=color1),\n",
    "                showlegend=(True if beta == constants_beta[0] else False)\n",
    "            ))\n",
    "\n",
    "        all_beta = wu.deg2rad(np.arange(-90, 91, 0.5))\n",
    "        all_beta[0] += 1e-8\n",
    "        all_beta[-1] -= 1e-8\n",
    "        constants_lamb = wu.deg2rad(np.arange(-180, 180, 15))\n",
    "        for lamb in constants_lamb:\n",
    "            if lamb != 0 and lamb != np.pi:\n",
    "                xyz = ell.ell2cart(all_beta, lamb)\n",
    "                fig.add_trace(go.Scatter3d(\n",
    "                    x=xyz[:, 0], y=xyz[:, 1], z=xyz[:, 2], mode=\"lines\", name=\"constant λ\",\n",
    "                    line=dict(width=linewidth, color=color2),\n",
    "                    showlegend=(True if lamb == constants_lamb[0] else False)\n",
    "                ))\n",
    "            else:\n",
    "                x, y, z = ell.para2cart(np.linspace(0, 2 * np.pi, 361), lamb)\n",
    "                fig.add_trace(go.Scatter3d(\n",
    "                    x=x, y=y, z=z, mode=\"lines\",\n",
    "                    line=dict(width=linewidth, color=\"black\"),\n",
    "                    showlegend=False\n",
    "                ))\n",
    "\n",
    "\n",
    "    elif coordsystem == \"geod\":\n",
    "        constants_phi = wu.deg2rad(np.arange(-90, 91, 15))\n",
    "        all_lamb = wu.deg2rad(np.arange(-180, 180, 0.5))\n",
    "        for phi in constants_phi:\n",
    "            x, y, z = ell.geod2cart(phi, all_lamb, 0)\n",
    "            fig.add_trace(go.Scatter3d(\n",
    "                x=x, y=y, z=z, mode=\"lines\",\n",
    "                line=dict(width=linewidth, color=color1), name=\"constant φ\",\n",
    "                showlegend=(True if phi == constants_phi[0] else False)\n",
    "            ))\n",
    "\n",
    "        all_phi = wu.deg2rad(np.arange(-90, 91, 0.5))\n",
    "        constants_lamb = wu.deg2rad(np.arange(-180, 180, 15))\n",
    "        for lamb in constants_lamb:\n",
    "            x, y, z = ell.geod2cart(all_phi, lamb, 0)\n",
    "            fig.add_trace(go.Scatter3d(\n",
    "                x=x, y=y, z=z, mode=\"lines\",\n",
    "                line=dict(width=linewidth, color=color2), name=\"constant λ\",\n",
    "                showlegend=(True if lamb == constants_lamb[0] else False)\n",
    "            ))\n",
    "\n",
    "    return fig"
   ],
   "id": "2d061b2f6ef6a78e",
   "outputs": [],
   "execution_count": null
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-02-04T08:51:31.257097Z",
     "start_time": "2026-02-04T08:51:31.242364Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def figure_points(fig, points):\n",
    "    \"\"\"\n",
    "\n",
    "    :param fig: plotly.graph_objects.Figure\n",
    "    :param points: Punktliste [(name, (x,y,z), color)]\n",
    "    :return: plotly.graph_objects.Figure\n",
    "    \"\"\"\n",
    "    for name, (px, py, pz), color in points:\n",
    "        fig.add_trace(go.Scatter3d(\n",
    "            x=[px], y=[py], z=[pz],\n",
    "            mode=\"markers+text\",\n",
    "            marker=dict(size=6, color=color),\n",
    "            text=[name], textposition=\"top center\",\n",
    "            name=name, showlegend=False\n",
    "        ))\n",
    "    return fig"
   ],
   "id": "92ab2e389d1ef948",
   "outputs": [],
   "execution_count": 21
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-02-04T08:51:31.291974Z",
     "start_time": "2026-02-04T08:51:31.274698Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def axis(fig, ell, L):\n",
    "    Lx = ell.ax + L\n",
    "    Ly = ell.ay + L\n",
    "    Lz = ell.b + L\n",
    "\n",
    "    # --- Achsenlinien ---\n",
    "    fig.add_trace(go.Scatter3d(\n",
    "        x=[0, Lx], y=[0, 0], z=[0, 0],\n",
    "        mode=\"lines\",\n",
    "        line=dict(width=6, color=\"black\"),\n",
    "        name=\"x\",\n",
    "        showlegend=False\n",
    "    ))\n",
    "\n",
    "    fig.add_trace(go.Scatter3d(\n",
    "        x=[0, 0], y=[0, Ly], z=[0, 0],\n",
    "        mode=\"lines\",\n",
    "        line=dict(width=6, color=\"black\"),\n",
    "        name=\"y\",\n",
    "        showlegend=False\n",
    "    ))\n",
    "\n",
    "    fig.add_trace(go.Scatter3d(\n",
    "        x=[0, 0], y=[0, 0], z=[0, Lz],\n",
    "        mode=\"lines\",\n",
    "        line=dict(width=6, color=\"black\"),\n",
    "        name=\"z\",\n",
    "        showlegend=False\n",
    "    ))\n",
    "\n",
    "    # --- Pfeilspitzen mit Cone ---\n",
    "    fig.add_trace(go.Cone(\n",
    "        x=[Lx], y=[0], z=[0],\n",
    "        u=[0.1], v=[0], w=[0],\n",
    "        sizemode=\"absolute\",\n",
    "        sizeref=0.2,\n",
    "        showscale=False,\n",
    "        showlegend=False,\n",
    "        colorscale=[[0, \"black\"], [1, \"black\"]]\n",
    "    ))\n",
    "\n",
    "    fig.add_trace(go.Cone(\n",
    "        x=[0], y=[Ly], z=[0],\n",
    "        u=[0], v=[0.1], w=[0],\n",
    "        sizemode=\"absolute\",\n",
    "        sizeref=0.2,\n",
    "        showscale=False,\n",
    "        showlegend=False,\n",
    "        colorscale=[[0, \"black\"], [1, \"black\"]]\n",
    "    ))\n",
    "\n",
    "    fig.add_trace(go.Cone(\n",
    "        x=[0], y=[0], z=[Lz],\n",
    "        u=[0], v=[0], w=[0.1],\n",
    "        sizemode=\"absolute\",\n",
    "        sizeref=0.2,\n",
    "        showscale=False,\n",
    "        showlegend=False,\n",
    "        colorscale=[[0, \"black\"], [1, \"black\"]]\n",
    "    ))\n",
    "\n",
    "    # --- Achsenbeschriftung ---\n",
    "    # fig.add_trace(go.Scatter3d(\n",
    "    #     x=[Lx], y=[0], z=[0.1],\n",
    "    #     mode=\"text\",\n",
    "    #     text=[\"X\"],\n",
    "    #     textposition=\"top center\",\n",
    "    #     showlegend=False\n",
    "    # ))\n",
    "    #\n",
    "    # fig.add_trace(go.Scatter3d(\n",
    "    #     x=[0], y=[Ly], z=[0.1],\n",
    "    #     mode=\"text\",\n",
    "    #     text=[\"Y\"],\n",
    "    #     textposition=\"top center\",\n",
    "    #     showlegend=False\n",
    "    # ))\n",
    "    #\n",
    "    # fig.add_trace(go.Scatter3d(\n",
    "    #     x=[0], y=[0], z=[Lz+0.1],\n",
    "    #     mode=\"text\",\n",
    "    #     text=[\"Z\"],\n",
    "    #     textposition=\"top center\",\n",
    "    #     showlegend=False\n",
    "    # ))\n",
    "    return fig"
   ],
   "id": "8a88218d1f3dd985",
   "outputs": [],
   "execution_count": 22
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-02-04T08:51:31.487219Z",
     "start_time": "2026-02-04T08:51:31.307922Z"
    }
   },
   "cell_type": "code",
   "source": [
    "ell = EllipsoidTriaxial.init_name(\"KarneyTest2024\")\n",
    "fig = ellipsoid_figure(ell, title=\"\", all=True, opac=1)\n",
    "# fig = figure_constant_lines(fig, ell, \"ell\", linewidth=5, color1=\"green\", color2=\"blue\")\n",
    "# fig = figure_constant_lines(fig, ell, \"para\", linewidth=5, color1=\"green\", color2=\"blue\")\n",
    "fig = figure_constant_lines(fig, ell, \"geod\", linewidth=5, color1=\"green\", color2=\"blue\")\n",
    "fig = axis(fig, ell, 0.2)\n",
    "fig.update_layout(\n",
    "    scene=dict(\n",
    "        xaxis=dict(showgrid=False, showline=False, zeroline=False, showticklabels=False, ticks=\"\"),\n",
    "        yaxis=dict(showgrid=False, showline=False, zeroline=False, showticklabels=False, ticks=\"\"),\n",
    "        zaxis=dict(showgrid=False, showline=False, zeroline=False, showticklabels=False, ticks=\"\"),\n",
    "        aspectmode=\"cube\"\n",
    "    ),\n",
    "    template=\"simple_white\",\n",
    ")\n",
    "fig.show()"
   ],
   "id": "d143ab42fa580a1b",
   "outputs": [
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         "opacity": 1,
         "showlegend": true,
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          "bdata": "[encoded data, 7704 characters]"
         },
         "z": {
          "dtype": "f8",
          "bdata": "[encoded data, 7704 characters]"
         },
         "type": "scatter3d"
        },
        {
         "line": {
          "color": "green",
          "width": 5
         },
         "mode": "lines",
         "name": "constant φ",
         "showlegend": false,
         "x": {
          "dtype": "f8",
          "bdata": "[encoded data, 7704 characters]"
         },
         "y": {
          "dtype": "f8",
          "bdata": "[encoded data, 7704 characters]"
         },
         "z": {
          "dtype": "f8",
          "bdata": "[encoded data, 7704 characters]"
         },
         "type": "scatter3d"
        },
        {
         "line": {
          "color": "blue",
          "width": 5
         },
         "mode": "lines",
         "name": "constant λ",
         "showlegend": true,
         "x": {
          "dtype": "f8",
          "bdata": "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"
         },
         "y": {
          "dtype": "f8",
          "bdata": "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"
         },
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         "type": "scatter3d"
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         "mode": "lines",
         "name": "constant λ",
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         "line": {
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          "width": 5
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         "mode": "lines",
         "name": "constant λ",
         "showlegend": false,
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         "type": "scatter3d"
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         "line": {
          "color": "blue",
          "width": 5
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         "mode": "lines",
         "name": "constant λ",
         "showlegend": false,
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         "type": "scatter3d"
        },
        {
         "line": {
          "color": "blue",
          "width": 5
         },
         "mode": "lines",
         "name": "constant λ",
         "showlegend": false,
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         "name": "constant λ",
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         "type": "scatter3d"
        },
        {
         "line": {
          "color": "blue",
          "width": 5
         },
         "mode": "lines",
         "name": "constant λ",
         "showlegend": false,
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         "type": "scatter3d"
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         "mode": "lines",
         "name": "constant λ",
         "showlegend": false,
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         "type": "scatter3d"
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         "line": {
          "color": "blue",
          "width": 5
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         "mode": "lines",
         "name": "constant λ",
         "showlegend": false,
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         "mode": "lines",
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         "line": {
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         "mode": "lines",
         "name": "constant λ",
         "showlegend": false,
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         "type": "scatter3d"
        },
        {
         "line": {
          "color": "blue",
          "width": 5
         },
         "mode": "lines",
         "name": "constant λ",
         "showlegend": false,
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         "type": "scatter3d"
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        {
         "line": {
          "color": "blue",
          "width": 5
         },
         "mode": "lines",
         "name": "constant λ",
         "showlegend": false,
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         "mode": "lines",
         "name": "constant λ",
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         "type": "scatter3d"
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        {
         "line": {
          "color": "blue",
          "width": 5
         },
         "mode": "lines",
         "name": "constant λ",
         "showlegend": false,
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         "type": "scatter3d"
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        {
         "line": {
          "color": "blue",
          "width": 5
         },
         "mode": "lines",
         "name": "constant λ",
         "showlegend": false,
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         "mode": "lines",
         "name": "constant λ",
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         "type": "scatter3d"
        },
        {
         "line": {
          "color": "blue",
          "width": 5
         },
         "mode": "lines",
         "name": "constant λ",
         "showlegend": false,
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   "metadata": {
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     "start_time": "2026-02-04T08:51:31.626372Z"
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   "source": [
    "ell = EllipsoidTriaxial.init_name(\"KarneyTest2024\")\n",
    "fig = ellipsoid_figure(ell, title=\"\", all=False, opac=0.7)\n",
    "fig = show_spere(fig, ell, all=False, opac=0.3)\n",
    "fig = axis(fig, ell, 0.2)\n",
    "fig.update_layout(\n",
    "    scene=dict(\n",
    "        xaxis=dict(showgrid=False, showline=False, zeroline=False, showticklabels=False, ticks=\"\"),\n",
    "        yaxis=dict(showgrid=False, showline=False, zeroline=False, showticklabels=False, ticks=\"\"),\n",
    "        zaxis=dict(showgrid=False, showline=False, zeroline=False, showticklabels=False, ticks=\"\"),\n",
    "        aspectmode=\"cube\"\n",
    "    ),\n",
    "    template=\"simple_white\",\n",
    ")\n",
    "\n",
    "r = ell.ax\n",
    "U = 0.4\n",
    "V = 1.1\n",
    "X = r * np.cos(U) * np.cos(V)\n",
    "Y = r * np.cos(U) * np.sin(V)\n",
    "Z = r * np.sin(U)\n",
    "P_sph = np.array([X, Y, Z])\n",
    "P_ell = ell.para2cart(U, V)\n",
    "\n",
    "\n",
    "# --- Helper: Pfeil (Schaft + Cone-Spitze) ---\n",
    "def add_arrow(fig, tail, head, color, name, line_width=6, head_px=0.25):\n",
    "    tail = np.asarray(tail, float)\n",
    "    head = np.asarray(head, float)\n",
    "    d = head - tail\n",
    "    norm = np.linalg.norm(d)\n",
    "    if norm < 1e-15:\n",
    "        return\n",
    "    u, v, w = (d / norm).tolist()\n",
    "\n",
    "    # Schaft\n",
    "    fig.add_trace(go.Scatter3d(\n",
    "        x=[tail[0], head[0]], y=[tail[1], head[1]], z=[tail[2], head[2]],\n",
    "        mode=\"lines\",\n",
    "        line=dict(width=line_width, color=color),\n",
    "        name=name,\n",
    "        showlegend=False\n",
    "    ))\n",
    "    # # Spitze\n",
    "    # fig.add_trace(go.Scatter3d(\n",
    "    #     x=[head[0]],\n",
    "    #     y=[head[1]],\n",
    "    #     z=[head[2]],\n",
    "    #     mode=\"markers\",\n",
    "    #     marker=dict(\n",
    "    #         size=head_px,\n",
    "    #         color=color,\n",
    "    #         symbol=\"diamond\"   # oder \"circle\"\n",
    "    #     ),\n",
    "    #     showlegend=False\n",
    "    # ))\n",
    "\n",
    "# --- Beide Punkte anzeigen ---\n",
    "fig.add_trace(go.Scatter3d(\n",
    "    x=[P_ell[0], P_sph[0]],\n",
    "    y=[P_ell[1], P_sph[1]],\n",
    "    z=[P_ell[2], P_sph[2]],\n",
    "    mode=\"markers+text\",\n",
    "    marker=dict(size=4, color=[\"orange\", \"red\"]),\n",
    "    # text=[\"P_ell\", \"P_sph\"],\n",
    "    textposition=\"top center\",\n",
    "    showlegend=False\n",
    "))\n",
    "\n",
    "# --- Rot: Pfeil von Durchstoßpunkt (XY-Ebene) zur Spitze auf der Normalen (P_G) ---\n",
    "add_arrow(fig, np.array([0, 0, 0]), P_sph, color=\"red\", name=\"Normal (XY→G)\", head_px=5, line_width=5)\n",
    "\n",
    "# --- Rot: Pfeil von Durchstoßpunkt (XY-Ebene) zur Spitze auf der Normalen (P_G) ---\n",
    "add_arrow(fig, np.array([0, 0, 0]), np.array([P_sph[0]*0.75, P_sph[1]*0.75, 0]), color=\"grey\", name=\"Normal (XY→G)\", head_px=5, line_width=3)\n",
    "\n",
    "# --- Orange: Pfeil zwischen den Punkten (P_E → P_G) ---\n",
    "add_arrow(fig, P_ell, P_sph, color=\"orange\", name=\"E→G\", head_px=5, line_width=3)\n",
    "fig.show()"
   ],
   "id": "f080fa54c95943e",
   "outputs": [
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