FromScratch/Grid_Encoding/3d_grid.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Grid Encoding (like Instant NGP)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as F\n",
    "import torch.optim as optim\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import plotly.graph_objects as go"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Our grid shape is torch.Size([10, 10, 10])\n"
     ]
    }
   ],
   "source": [
    "grid_size = 10\n",
    "device = torch.device(\"mps\")\n",
    "grid = torch.ones((grid_size, grid_size, grid_size)).to(device)\n",
    "print(f\"Our grid shape is {grid.shape}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Creating a plot to visualize the grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "plotlyServerURL": "https://plot.ly"
       },
       "data": [
        {
         "marker": {
          "color": [
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1
          ],
          "colorscale": [
           [
            0,
            "#440154"
           ],
           [
            0.1111111111111111,
            "#482878"
           ],
           [
            0.2222222222222222,
            "#3e4989"
           ],
           [
            0.3333333333333333,
            "#31688e"
           ],
           [
            0.4444444444444444,
            "#26828e"
           ],
           [
            0.5555555555555556,
            "#1f9e89"
           ],
           [
            0.6666666666666666,
            "#35b779"
           ],
           [
            0.7777777777777778,
            "#6ece58"
           ],
           [
            0.8888888888888888,
            "#b5de2b"
           ],
           [
            1,
            "#fde725"
           ]
          ],
          "opacity": 0.8,
          "size": 5
         },
         "mode": "markers",
         "type": "scatter3d",
         "x": [
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9
         ],
         "y": [
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9
         ],
         "z": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9
         ]
        }
       ],
       "layout": {
        "scene": {
         "xaxis": {
          "title": {
           "text": "X"
          }
         },
         "yaxis": {
          "title": {
           "text": "Y"
          }
         },
         "zaxis": {
          "title": {
           "text": "Z"
          }
         }
        },
        "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"
           }
          ],
          "mesh3d": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "mesh3d"
           }
          ],
          "parcoords": [
           {
            "line": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "parcoords"
           }
          ],
          "pie": [
           {
            "automargin": true,
            "type": "pie"
           }
          ],
          "scatter": [
           {
            "fillpattern": {
             "fillmode": "overlay",
             "size": 10,
             "solidity": 0.2
            },
            "type": "scatter"
           }
          ],
          "scatter3d": [
           {
            "line": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatter3d"
           }
          ],
          "scattercarpet": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattercarpet"
           }
          ],
          "scattergeo": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattergeo"
           }
          ],
          "scattergl": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattergl"
           }
          ],
          "scattermapbox": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattermapbox"
           }
          ],
          "scatterpolar": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterpolar"
           }
          ],
          "scatterpolargl": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterpolargl"
           }
          ],
          "scatterternary": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterternary"
           }
          ],
          "surface": [
           {
            "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": "surface"
           }
          ],
          "table": [
           {
            "cells": {
             "fill": {
              "color": "#EBF0F8"
             },
             "line": {
              "color": "white"
             }
            },
            "header": {
             "fill": {
              "color": "#C8D4E3"
             },
             "line": {
              "color": "white"
             }
            },
            "type": "table"
           }
          ]
         },
         "layout": {
          "annotationdefaults": {
           "arrowcolor": "#2a3f5f",
           "arrowhead": 0,
           "arrowwidth": 1
          },
          "autotypenumbers": "strict",
          "coloraxis": {
           "colorbar": {
            "outlinewidth": 0,
            "ticks": ""
           }
          },
          "colorscale": {
           "diverging": [
            [
             0,
             "#8e0152"
            ],
            [
             0.1,
             "#c51b7d"
            ],
            [
             0.2,
             "#de77ae"
            ],
            [
             0.3,
             "#f1b6da"
            ],
            [
             0.4,
             "#fde0ef"
            ],
            [
             0.5,
             "#f7f7f7"
            ],
            [
             0.6,
             "#e6f5d0"
            ],
            [
             0.7,
             "#b8e186"
            ],
            [
             0.8,
             "#7fbc41"
            ],
            [
             0.9,
             "#4d9221"
            ],
            [
             1,
             "#276419"
            ]
           ],
           "sequential": [
            [
             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"
            ]
           ],
           "sequentialminus": [
            [
             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"
            ]
           ]
          },
          "colorway": [
           "#636efa",
           "#EF553B",
           "#00cc96",
           "#ab63fa",
           "#FFA15A",
           "#19d3f3",
           "#FF6692",
           "#B6E880",
           "#FF97FF",
           "#FECB52"
          ],
          "font": {
           "color": "#2a3f5f"
          },
          "geo": {
           "bgcolor": "white",
           "lakecolor": "white",
           "landcolor": "#E5ECF6",
           "showlakes": true,
           "showland": true,
           "subunitcolor": "white"
          },
          "hoverlabel": {
           "align": "left"
          },
          "hovermode": "closest",
          "mapbox": {
           "style": "light"
          },
          "paper_bgcolor": "white",
          "plot_bgcolor": "#E5ECF6",
          "polar": {
           "angularaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "radialaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "scene": {
           "xaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "yaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "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
          }
         }
        },
        "title": {
         "text": "3D Random Grid Visualization"
        }
       }
      }
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "grid_np = grid.cpu().numpy()\n",
    "\n",
    "x, y, z = np.indices(grid_np.shape)\n",
    "values = grid_np.flatten()\n",
    "\n",
    "fig = go.Figure(\n",
    "    data=go.Scatter3d(\n",
    "        x=x.flatten(),\n",
    "        y=y.flatten(),\n",
    "        z=z.flatten(),\n",
    "        mode=\"markers\",\n",
    "        marker=dict(size=5, color=values, colorscale=\"Viridis\", opacity=0.8),\n",
    "    )\n",
    ")\n",
    "\n",
    "fig.update_layout(\n",
    "    title=\"3D Random Grid Visualization\",\n",
    "    scene=dict(xaxis_title=\"X\", yaxis_title=\"Y\", zaxis_title=\"Z\"),\n",
    ")\n",
    "\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualizing a sample 3D point"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([2.2381, 5.5359, 5.5115])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample_point = torch.rand(3) * grid_size\n",
    "sample_point"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "plotlyServerURL": "https://plot.ly"
       },
       "data": [
        {
         "marker": {
          "color": [
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1
          ],
          "colorscale": [
           [
            0,
            "#440154"
           ],
           [
            0.1111111111111111,
            "#482878"
           ],
           [
            0.2222222222222222,
            "#3e4989"
           ],
           [
            0.3333333333333333,
            "#31688e"
           ],
           [
            0.4444444444444444,
            "#26828e"
           ],
           [
            0.5555555555555556,
            "#1f9e89"
           ],
           [
            0.6666666666666666,
            "#35b779"
           ],
           [
            0.7777777777777778,
            "#6ece58"
           ],
           [
            0.8888888888888888,
            "#b5de2b"
           ],
           [
            1,
            "#fde725"
           ]
          ],
          "opacity": 0.8,
          "size": 5
         },
         "mode": "markers",
         "type": "scatter3d",
         "x": [
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9
         ],
         "y": [
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9
         ],
         "z": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9
         ]
        },
        {
         "marker": {
          "color": "red",
          "opacity": 0.5,
          "size": 3
         },
         "mode": "markers",
         "type": "scatter3d",
         "x": [
          2.2380967140197754
         ],
         "y": [
          5.535866737365723
         ],
         "z": [
          5.511519432067871
         ]
        }
       ],
       "layout": {
        "scene": {
         "xaxis": {
          "title": {
           "text": "X"
          }
         },
         "yaxis": {
          "title": {
           "text": "Y"
          }
         },
         "zaxis": {
          "title": {
           "text": "Z"
          }
         }
        },
        "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"
           }
          ],
          "mesh3d": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "mesh3d"
           }
          ],
          "parcoords": [
           {
            "line": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "parcoords"
           }
          ],
          "pie": [
           {
            "automargin": true,
            "type": "pie"
           }
          ],
          "scatter": [
           {
            "fillpattern": {
             "fillmode": "overlay",
             "size": 10,
             "solidity": 0.2
            },
            "type": "scatter"
           }
          ],
          "scatter3d": [
           {
            "line": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatter3d"
           }
          ],
          "scattercarpet": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattercarpet"
           }
          ],
          "scattergeo": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattergeo"
           }
          ],
          "scattergl": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattergl"
           }
          ],
          "scattermapbox": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattermapbox"
           }
          ],
          "scatterpolar": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterpolar"
           }
          ],
          "scatterpolargl": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterpolargl"
           }
          ],
          "scatterternary": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterternary"
           }
          ],
          "surface": [
           {
            "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": "surface"
           }
          ],
          "table": [
           {
            "cells": {
             "fill": {
              "color": "#EBF0F8"
             },
             "line": {
              "color": "white"
             }
            },
            "header": {
             "fill": {
              "color": "#C8D4E3"
             },
             "line": {
              "color": "white"
             }
            },
            "type": "table"
           }
          ]
         },
         "layout": {
          "annotationdefaults": {
           "arrowcolor": "#2a3f5f",
           "arrowhead": 0,
           "arrowwidth": 1
          },
          "autotypenumbers": "strict",
          "coloraxis": {
           "colorbar": {
            "outlinewidth": 0,
            "ticks": ""
           }
          },
          "colorscale": {
           "diverging": [
            [
             0,
             "#8e0152"
            ],
            [
             0.1,
             "#c51b7d"
            ],
            [
             0.2,
             "#de77ae"
            ],
            [
             0.3,
             "#f1b6da"
            ],
            [
             0.4,
             "#fde0ef"
            ],
            [
             0.5,
             "#f7f7f7"
            ],
            [
             0.6,
             "#e6f5d0"
            ],
            [
             0.7,
             "#b8e186"
            ],
            [
             0.8,
             "#7fbc41"
            ],
            [
             0.9,
             "#4d9221"
            ],
            [
             1,
             "#276419"
            ]
           ],
           "sequential": [
            [
             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"
            ]
           ],
           "sequentialminus": [
            [
             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"
            ]
           ]
          },
          "colorway": [
           "#636efa",
           "#EF553B",
           "#00cc96",
           "#ab63fa",
           "#FFA15A",
           "#19d3f3",
           "#FF6692",
           "#B6E880",
           "#FF97FF",
           "#FECB52"
          ],
          "font": {
           "color": "#2a3f5f"
          },
          "geo": {
           "bgcolor": "white",
           "lakecolor": "white",
           "landcolor": "#E5ECF6",
           "showlakes": true,
           "showland": true,
           "subunitcolor": "white"
          },
          "hoverlabel": {
           "align": "left"
          },
          "hovermode": "closest",
          "mapbox": {
           "style": "light"
          },
          "paper_bgcolor": "white",
          "plot_bgcolor": "#E5ECF6",
          "polar": {
           "angularaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "radialaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "scene": {
           "xaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "yaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "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
          }
         }
        },
        "title": {
         "text": "3D Random Grid Visualization"
        }
       }
      }
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig.add_trace(go.Scatter3d(\n",
    "    x=[sample_point[0]],\n",
    "    y=[sample_point[1]],\n",
    "    z=[sample_point[2]],\n",
    "    mode='markers',\n",
    "    marker=dict(\n",
    "        size=3,\n",
    "        color='red',\n",
    "        opacity=0.5\n",
    "    )\n",
    "))\n",
    "\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Finding vertices of the nearest voxel grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def return_corresponding_voxel_vertices(sample_points):\n",
    "    sample_points = sample_points.to(device)\n",
    "    lower_1 = torch.floor(sample_points)\n",
    "    upper_1 = torch.ceil(sample_points)\n",
    "    lower_2 = lower_1 + torch.tensor([0, 0, 1]).to(device)\n",
    "    lower_3 = lower_1 + torch.tensor([0, 1, 0]).to(device)\n",
    "    lower_4 = lower_1 + torch.tensor([1, 0, 0]).to(device)\n",
    "    upper_2 = upper_1 - torch.tensor([0, 0, 1]).to(device)\n",
    "    upper_3 = upper_1 - torch.tensor([0, 1, 0]).to(device)\n",
    "    upper_4 = upper_1 - torch.tensor([1, 0, 0]).to(device)\n",
    "    return torch.stack(\n",
    "        [lower_1, upper_1, lower_2, lower_3, lower_4, upper_2, upper_3, upper_4], dim=1\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([4, 8, 3])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "return_corresponding_voxel_vertices(torch.rand((4, 3)) * grid_size).shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualizing a sample 3D point and its nearest voxel grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "sample_voxel_vertices = (\n",
    "    return_corresponding_voxel_vertices(sample_point.unsqueeze(0)).cpu().numpy()\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "plotlyServerURL": "https://plot.ly"
       },
       "data": [
        {
         "marker": {
          "color": [
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1,
           1
          ],
          "colorscale": [
           [
            0,
            "#440154"
           ],
           [
            0.1111111111111111,
            "#482878"
           ],
           [
            0.2222222222222222,
            "#3e4989"
           ],
           [
            0.3333333333333333,
            "#31688e"
           ],
           [
            0.4444444444444444,
            "#26828e"
           ],
           [
            0.5555555555555556,
            "#1f9e89"
           ],
           [
            0.6666666666666666,
            "#35b779"
           ],
           [
            0.7777777777777778,
            "#6ece58"
           ],
           [
            0.8888888888888888,
            "#b5de2b"
           ],
           [
            1,
            "#fde725"
           ]
          ],
          "opacity": 0.8,
          "size": 5
         },
         "mode": "markers",
         "type": "scatter3d",
         "x": [
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9
         ],
         "y": [
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          4,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          5,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          7,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          8,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9,
          9
         ],
         "z": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9
         ]
        },
        {
         "marker": {
          "color": "red",
          "opacity": 0.5,
          "size": 3
         },
         "mode": "markers",
         "type": "scatter3d",
         "x": [
          2.2380967140197754
         ],
         "y": [
          5.535866737365723
         ],
         "z": [
          5.511519432067871
         ]
        },
        {
         "marker": {
          "color": "blue",
          "opacity": 1,
          "size": 5
         },
         "mode": "markers",
         "type": "scatter3d",
         "x": [
          2,
          3,
          2,
          2,
          3,
          3,
          3,
          2
         ],
         "y": [
          5,
          6,
          5,
          6,
          5,
          6,
          5,
          6
         ],
         "z": [
          5,
          6,
          6,
          5,
          5,
          5,
          6,
          6
         ]
        }
       ],
       "layout": {
        "scene": {
         "xaxis": {
          "title": {
           "text": "X"
          }
         },
         "yaxis": {
          "title": {
           "text": "Y"
          }
         },
         "zaxis": {
          "title": {
           "text": "Z"
          }
         }
        },
        "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"
           }
          ],
          "mesh3d": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "mesh3d"
           }
          ],
          "parcoords": [
           {
            "line": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "parcoords"
           }
          ],
          "pie": [
           {
            "automargin": true,
            "type": "pie"
           }
          ],
          "scatter": [
           {
            "fillpattern": {
             "fillmode": "overlay",
             "size": 10,
             "solidity": 0.2
            },
            "type": "scatter"
           }
          ],
          "scatter3d": [
           {
            "line": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatter3d"
           }
          ],
          "scattercarpet": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattercarpet"
           }
          ],
          "scattergeo": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattergeo"
           }
          ],
          "scattergl": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattergl"
           }
          ],
          "scattermapbox": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattermapbox"
           }
          ],
          "scatterpolar": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterpolar"
           }
          ],
          "scatterpolargl": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterpolargl"
           }
          ],
          "scatterternary": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterternary"
           }
          ],
          "surface": [
           {
            "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": "surface"
           }
          ],
          "table": [
           {
            "cells": {
             "fill": {
              "color": "#EBF0F8"
             },
             "line": {
              "color": "white"
             }
            },
            "header": {
             "fill": {
              "color": "#C8D4E3"
             },
             "line": {
              "color": "white"
             }
            },
            "type": "table"
           }
          ]
         },
         "layout": {
          "annotationdefaults": {
           "arrowcolor": "#2a3f5f",
           "arrowhead": 0,
           "arrowwidth": 1
          },
          "autotypenumbers": "strict",
          "coloraxis": {
           "colorbar": {
            "outlinewidth": 0,
            "ticks": ""
           }
          },
          "colorscale": {
           "diverging": [
            [
             0,
             "#8e0152"
            ],
            [
             0.1,
             "#c51b7d"
            ],
            [
             0.2,
             "#de77ae"
            ],
            [
             0.3,
             "#f1b6da"
            ],
            [
             0.4,
             "#fde0ef"
            ],
            [
             0.5,
             "#f7f7f7"
            ],
            [
             0.6,
             "#e6f5d0"
            ],
            [
             0.7,
             "#b8e186"
            ],
            [
             0.8,
             "#7fbc41"
            ],
            [
             0.9,
             "#4d9221"
            ],
            [
             1,
             "#276419"
            ]
           ],
           "sequential": [
            [
             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"
            ]
           ],
           "sequentialminus": [
            [
             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"
            ]
           ]
          },
          "colorway": [
           "#636efa",
           "#EF553B",
           "#00cc96",
           "#ab63fa",
           "#FFA15A",
           "#19d3f3",
           "#FF6692",
           "#B6E880",
           "#FF97FF",
           "#FECB52"
          ],
          "font": {
           "color": "#2a3f5f"
          },
          "geo": {
           "bgcolor": "white",
           "lakecolor": "white",
           "landcolor": "#E5ECF6",
           "showlakes": true,
           "showland": true,
           "subunitcolor": "white"
          },
          "hoverlabel": {
           "align": "left"
          },
          "hovermode": "closest",
          "mapbox": {
           "style": "light"
          },
          "paper_bgcolor": "white",
          "plot_bgcolor": "#E5ECF6",
          "polar": {
           "angularaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "radialaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "scene": {
           "xaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "yaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "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
          }
         }
        },
        "title": {
         "text": "3D Random Grid Visualization"
        }
       }
      }
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig.add_trace(\n",
    "    go.Scatter3d(\n",
    "        x=sample_voxel_vertices[0, :, 0],\n",
    "        y=sample_voxel_vertices[0, :, 1],\n",
    "        z=sample_voxel_vertices[0, :, 2],\n",
    "        mode=\"markers\",\n",
    "        marker=dict(size=5, color=\"blue\", opacity=1),\n",
    "    )\n",
    ")\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Creating embeddings for each vertex of voxels in the 3D grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([1000, 4])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Feature_dim = 4\n",
    "embedding = nn.Embedding(grid_size * grid_size * grid_size, Feature_dim).to(device)\n",
    "embedding.weight.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Interpolation function\n",
    "(for getting the embeddings of any point in 3D space as sum of weighted embeddings of the nearest voxel grid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def interpolate(sample_points, embedding, type=\"Linear\"):\n",
    "    sample_points = sample_points.to(device)\n",
    "    batch_size = sample_points.shape[0]\n",
    "    vertices_of_interest = return_corresponding_voxel_vertices(sample_points)\n",
    "    flattened_indices = (\n",
    "        (\n",
    "            vertices_of_interest[:, :, 0]\n",
    "            + grid_size * vertices_of_interest[:, :, 1]\n",
    "            + grid_size * grid_size * vertices_of_interest[:, :, 2]\n",
    "        )\n",
    "        .long()\n",
    "        .to(device)\n",
    "    )\n",
    "    embeddings = embedding(flattened_indices).squeeze()\n",
    "    distances = torch.norm(vertices_of_interest - sample_points.unsqueeze(1), dim=2)\n",
    "    if type == \"Linear\":\n",
    "        weights = 1 / distances\n",
    "    else:\n",
    "        raise NotImplementedError\n",
    "\n",
    "    weights = weights / torch.sum(weights, dim=1, keepdim=True)\n",
    "    weights = weights.unsqueeze(2)\n",
    "    return torch.sum(embeddings * weights, dim=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A sample down-stream task (SDF prediction) using the embeddings"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Creating a dataset of sphere SDFs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "from torch.utils.data import DataLoader, TensorDataset\n",
    "from torch.utils.data.dataset import random_split\n",
    "\n",
    "\n",
    "def sphere_sdf(x, y, z):\n",
    "    return torch.sqrt((x - 2) ** 2 + (y - 2) ** 2 + (z - 2) ** 2) - 0.5\n",
    "\n",
    "\n",
    "sample_size = 2**15\n",
    "random_points_in_grid = torch.rand(sample_size, 3) * grid_size\n",
    "gt_sdf_vals = sphere_sdf(\n",
    "    random_points_in_grid[:, 0],\n",
    "    random_points_in_grid[:, 1],\n",
    "    random_points_in_grid[:, 2],\n",
    ").to(device)\n",
    "random_points_in_grid = random_points_in_grid.to(device)\n",
    "\n",
    "points_dataset = TensorDataset(random_points_in_grid, gt_sdf_vals)\n",
    "train_size = int(0.8 * sample_size)\n",
    "val_size = sample_size - train_size\n",
    "train_dataset, val_dataset = random_split(points_dataset, [train_size, val_size])\n",
    "\n",
    "BATCH_SIZE = 64\n",
    "train_loader = DataLoader(train_dataset, batch_size=BATCH_SIZE, shuffle=True)\n",
    "val_loader = DataLoader(val_dataset, batch_size=BATCH_SIZE, shuffle=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Training loop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/100 [00:00<?, ?it/s]"
     ]
    }
   ],
   "source": [
    "from tqdm import tqdm\n",
    "\n",
    "model = nn.Sequential(\n",
    "    nn.Linear(Feature_dim, 256),\n",
    "    nn.ReLU(),\n",
    "    nn.Linear(256, 256),\n",
    "    nn.ReLU(),\n",
    "    nn.Linear(256, 1),\n",
    ").to(device)\n",
    "\n",
    "optimizer = optim.Adam(list(model.parameters()) + list(embedding.parameters()), lr=1e-3)\n",
    "EPOCHS = 100\n",
    "pbar = tqdm(range(int(EPOCHS)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Epoch 1:   1%|          | 1/100 [00:05<08:38,  5.23s/it, Loss=3.06]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 0 - Val Loss: 3.597395896911621\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Epoch 11:  11%|█         | 11/100 [00:44<05:50,  3.93s/it, Loss=0.199]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 10 - Val Loss: 0.2925286293029785\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Epoch 21:  21%|██        | 21/100 [01:22<05:11,  3.95s/it, Loss=0.0921]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 20 - Val Loss: 0.14235101640224457\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Epoch 31:  31%|███       | 31/100 [02:01<04:35,  3.99s/it, Loss=0.0463]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 30 - Val Loss: 0.08255120366811752\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Epoch 41:  41%|████      | 41/100 [02:40<04:02,  4.11s/it, Loss=0.0449]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 40 - Val Loss: 0.06785129010677338\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Epoch 51:  51%|█████     | 51/100 [03:21<03:19,  4.06s/it, Loss=0.0537]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 50 - Val Loss: 0.05200814828276634\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Epoch 61:  61%|██████    | 61/100 [04:02<02:48,  4.31s/it, Loss=0.0232]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 60 - Val Loss: 0.04541991651058197\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Epoch 71:  71%|███████   | 71/100 [04:45<02:07,  4.40s/it, Loss=0.026] "
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 70 - Val Loss: 0.04362420365214348\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Epoch 81:  81%|████████  | 81/100 [05:24<01:17,  4.08s/it, Loss=0.0228]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 80 - Val Loss: 0.04999928921461105\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Epoch 91:  91%|█████████ | 91/100 [06:05<00:39,  4.37s/it, Loss=0.0171]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 90 - Val Loss: 0.04161970317363739\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Epoch 99: 100%|██████████| 100/100 [06:43<00:00,  4.03s/it, Loss=0.0331]\n"
     ]
    }
   ],
   "source": [
    "for epoch in pbar:\n",
    "    pbar.set_description(f\"Epoch {epoch}\")\n",
    "    for i, (x, sdf_val) in enumerate(train_loader):\n",
    "        optimizer.zero_grad()\n",
    "        y_pred = model(interpolate(x, embedding))\n",
    "        loss = F.mse_loss(y_pred, sdf_val.unsqueeze(1))\n",
    "        loss.backward()\n",
    "        optimizer.step()\n",
    "        pbar.set_postfix({\"Loss\": loss.item()})\n",
    "\n",
    "    if epoch % 10 == 0:\n",
    "        with torch.no_grad():\n",
    "            val_loss = 0\n",
    "            for i, (x, y) in enumerate(val_loader):\n",
    "                y_pred = model(interpolate(x, embedding))\n",
    "                val_loss += F.mse_loss(y_pred, y.unsqueeze(1))\n",
    "            print(f\"Epoch {epoch} - Val Loss: {val_loss / len(val_loader)}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "temp",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}