{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Spatial analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import movekit as mkit\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.spatial import Voronoi, voronoi_plot_2d, convex_hull_plot_2d, delaunay_plot_2d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Extracting all absolute features: 100%|██████████| 100.0/100 [00:01<00:00, 81.44it/s]\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>time</th>\n",
       "      <th>animal_id</th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>distance</th>\n",
       "      <th>direction</th>\n",
       "      <th>turning</th>\n",
       "      <th>average_speed</th>\n",
       "      <th>average_acceleration</th>\n",
       "      <th>stopped</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>312</td>\n",
       "      <td>405.29</td>\n",
       "      <td>417.76</td>\n",
       "      <td>0.0</td>\n",
       "      <td>(0.0, 0.0)</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.210217</td>\n",
       "      <td>-0.006079</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>511</td>\n",
       "      <td>369.99</td>\n",
       "      <td>428.78</td>\n",
       "      <td>0.0</td>\n",
       "      <td>(0.0, 0.0)</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.020944</td>\n",
       "      <td>0.000041</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>607</td>\n",
       "      <td>390.33</td>\n",
       "      <td>405.89</td>\n",
       "      <td>0.0</td>\n",
       "      <td>(0.0, 0.0)</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.070235</td>\n",
       "      <td>0.000344</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>811</td>\n",
       "      <td>445.15</td>\n",
       "      <td>411.94</td>\n",
       "      <td>0.0</td>\n",
       "      <td>(0.0, 0.0)</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.370500</td>\n",
       "      <td>0.007092</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>905</td>\n",
       "      <td>366.06</td>\n",
       "      <td>451.76</td>\n",
       "      <td>0.0</td>\n",
       "      <td>(0.0, 0.0)</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.118000</td>\n",
       "      <td>-0.003975</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   time  animal_id       x       y  distance   direction  turning  \\\n",
       "0     1        312  405.29  417.76       0.0  (0.0, 0.0)      0.0   \n",
       "1     1        511  369.99  428.78       0.0  (0.0, 0.0)      0.0   \n",
       "2     1        607  390.33  405.89       0.0  (0.0, 0.0)      0.0   \n",
       "3     1        811  445.15  411.94       0.0  (0.0, 0.0)      0.0   \n",
       "4     1        905  366.06  451.76       0.0  (0.0, 0.0)      0.0   \n",
       "\n",
       "   average_speed  average_acceleration  stopped  \n",
       "0       0.210217             -0.006079        1  \n",
       "1       0.020944              0.000041        1  \n",
       "2       0.070235              0.000344        1  \n",
       "3       0.370500              0.007092        1  \n",
       "4       0.118000             -0.003975        1  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path = \"datasets/fish-5-cleaned.csv\"\n",
    "data = mkit.read_data(path)\n",
    "data = mkit.extract_features(data)\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Spatial Objects\n",
    "The function below produces three types of spatial objects: Voronoi-Diagrams, Convex Hulls and Delaunay Triangles. Optionally, one may obtain only group-specific outputs - one object per time-capture. These spatial objects may be used for a set of attributes, which are described below in detail.\n",
    "To get the full functionality of all attributes, please go to https://docs.scipy.org/doc/scipy-0.14.0/reference/tutorial/spatial.html."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Calculating spatial objects: 100%|██████████| 1000/1000 [00:15<00:00, 63.51it/s]\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>time</th>\n",
       "      <th>convex_hull_object</th>\n",
       "      <th>voronoi_object</th>\n",
       "      <th>delaunay_object</th>\n",
       "      <th>convex_hull_volume</th>\n",
       "      <th>voronoi_volume</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>&lt;scipy.spatial.qhull.ConvexHull object at 0x7f...</td>\n",
       "      <td>&lt;scipy.spatial.qhull.Voronoi object at 0x7ff88...</td>\n",
       "      <td>&lt;scipy.spatial.qhull.Delaunay object at 0x7ff8...</td>\n",
       "      <td>1519.44120</td>\n",
       "      <td>inf</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>&lt;scipy.spatial.qhull.ConvexHull object at 0x7f...</td>\n",
       "      <td>&lt;scipy.spatial.qhull.Voronoi object at 0x7ff88...</td>\n",
       "      <td>&lt;scipy.spatial.qhull.Delaunay object at 0x7ff8...</td>\n",
       "      <td>1528.95525</td>\n",
       "      <td>inf</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>&lt;scipy.spatial.qhull.ConvexHull object at 0x7f...</td>\n",
       "      <td>&lt;scipy.spatial.qhull.Voronoi object at 0x7ff88...</td>\n",
       "      <td>&lt;scipy.spatial.qhull.Delaunay object at 0x7ff8...</td>\n",
       "      <td>1539.23800</td>\n",
       "      <td>inf</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>&lt;scipy.spatial.qhull.ConvexHull object at 0x7f...</td>\n",
       "      <td>&lt;scipy.spatial.qhull.Voronoi object at 0x7ff88...</td>\n",
       "      <td>&lt;scipy.spatial.qhull.Delaunay object at 0x7ff8...</td>\n",
       "      <td>1549.61380</td>\n",
       "      <td>inf</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>&lt;scipy.spatial.qhull.ConvexHull object at 0x7f...</td>\n",
       "      <td>&lt;scipy.spatial.qhull.Voronoi object at 0x7ff88...</td>\n",
       "      <td>&lt;scipy.spatial.qhull.Delaunay object at 0x7ff8...</td>\n",
       "      <td>1560.33905</td>\n",
       "      <td>inf</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   time                                 convex_hull_object  \\\n",
       "0     1  <scipy.spatial.qhull.ConvexHull object at 0x7f...   \n",
       "1     2  <scipy.spatial.qhull.ConvexHull object at 0x7f...   \n",
       "2     3  <scipy.spatial.qhull.ConvexHull object at 0x7f...   \n",
       "3     4  <scipy.spatial.qhull.ConvexHull object at 0x7f...   \n",
       "4     5  <scipy.spatial.qhull.ConvexHull object at 0x7f...   \n",
       "\n",
       "                                      voronoi_object  \\\n",
       "0  <scipy.spatial.qhull.Voronoi object at 0x7ff88...   \n",
       "1  <scipy.spatial.qhull.Voronoi object at 0x7ff88...   \n",
       "2  <scipy.spatial.qhull.Voronoi object at 0x7ff88...   \n",
       "3  <scipy.spatial.qhull.Voronoi object at 0x7ff88...   \n",
       "4  <scipy.spatial.qhull.Voronoi object at 0x7ff88...   \n",
       "\n",
       "                                     delaunay_object  convex_hull_volume  \\\n",
       "0  <scipy.spatial.qhull.Delaunay object at 0x7ff8...          1519.44120   \n",
       "1  <scipy.spatial.qhull.Delaunay object at 0x7ff8...          1528.95525   \n",
       "2  <scipy.spatial.qhull.Delaunay object at 0x7ff8...          1539.23800   \n",
       "3  <scipy.spatial.qhull.Delaunay object at 0x7ff8...          1549.61380   \n",
       "4  <scipy.spatial.qhull.Delaunay object at 0x7ff8...          1560.33905   \n",
       "\n",
       "   voronoi_volume  \n",
       "0             inf  \n",
       "1             inf  \n",
       "2             inf  \n",
       "3             inf  \n",
       "4             inf  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "spatial_obj = mkit.get_spatial_objects(data, group_output = True)\n",
    "spatial_obj.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### Producing a voronoi diagram\n",
    "Each timestep gets a voronoi object as well as the area of the voronoi - shape. Infinity, if respective animal is outmost in swarm.\n",
    "\n",
    "Voronoi object contains the following attributes:\n",
    "\n",
    "- `points` Coordinates of input points.\n",
    "\n",
    "- `vertices` Coordinates of the Voronoi vertices.\n",
    "\n",
    "- `ridge_points` Indices of the points between which each Voronoi ridge lies.\n",
    "\n",
    "- `ridge_vertices` Indices of the Voronoi vertices forming each Voronoi ridge.\n",
    "\n",
    "- `regions` Indices of the Voronoi vertices forming each Voronoi region. -1 indicates vertex outside the Voronoi diagram.\n",
    "\n",
    "- `point_region` Index of the Voronoi region for each input point. If qhull option “Qc” was not specified, the list will contain -1 for points that are not associated with a Voronoi region.\n",
    "\n",
    "- `furthest_site` True if this was a furthest site triangulation and False if not.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Producing a convex hull\n",
    "Similar to voronoi-diagram, also the convex hull is of interest for movement-related data. Additionally, a set of attributes may be attached to the convex hull objects. Examples are:\n",
    "\n",
    "- `points` (array of ints) Coordinates of input points\n",
    "\n",
    "- `vertices` (array of ints ) Point indices forming the veritces of the convex hull\n",
    "\n",
    "- `area` Area of the convex hull.\n",
    "\n",
    "- `volume` Volume of the convex hull."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Producing Delaunay-triangles\n",
    "Examples for attributes of interest consist of:\n",
    "\n",
    "- `transform`\tAffine transform from x to the barycentric coordinates c.\n",
    "- `vertex_to_simplex`\tLookup array, from a vertex, to some simplex which it is a part of.\n",
    "- `convex_hull`\tVertices of facets forming the convex hull of the point set.\n",
    "- `vertex_neighbor_vertices`\tNeighboring vertices of vertices.\n",
    "- `points`\t(ndarray of double, shape (npoints, ndim)) Coordinates of input points.\n",
    "- `simplices`\t(ndarray of ints, shape (nsimplex, ndim+1)) Indices of the points forming the simplices in the triangulation. For 2-D, the points are oriented counterclockwise.\n",
    "- `neighbors`\t(ndarray of ints, shape (nsimplex, ndim+1)) Indices of neighbor simplices for each simplex. The kth neighbor is opposite to the kth vertex. For simplices at the boundary, -1 denotes no neighbor. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plotting all spatial objects at the 3rd timestep. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot all scipy - spatial objects of a given timestamp\n",
    "voronoi_plot_2d(spatial_obj.voronoi_object[2])\n",
    "convex_hull_plot_2d(spatial_obj.convex_hull_object[2])\n",
    "delaunay_plot_2d(spatial_obj.delaunay_object[2])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}