edge_length.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "982e10d5-356a-4642-983e-71cdfdbe7028",
   "metadata": {},
   "source": [
    "# Compute average H3 *cell* edge length\n",
    "\n",
    "- all edges considered, even those shared between pentagons and hexagons"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f3cb90a3-224a-4b61-916f-09f43c9911ed",
   "metadata": {},
   "outputs": [],
   "source": [
    "import h3.api.numpy_int as h3\n",
    "\n",
    "import time\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def edges_at_res(res):\n",
    "    cells0 = h3.get_res0_cells()\n",
    "    cells = h3.uncompact_cells(cells0, res)\n",
    "    edges = (\n",
    "        e\n",
    "        for c in cells\n",
    "        for e in h3.origin_to_directed_edges(c)\n",
    "    )\n",
    "    \n",
    "    yield from edges\n",
    "    \n",
    "def avg_edge_len_at_res(res, unit='km'):\n",
    "    tic = time.time()\n",
    "    i = 0\n",
    "    total = 0.0\n",
    "    for e in edges_at_res(res):\n",
    "        i += 1\n",
    "        total += h3.edge_length(e, unit=unit)\n",
    "    toc = time.time()\n",
    "    \n",
    "    print(f'Time for {res=:2}: {(toc-tic)/60.0:0.2f} minutes.')\n",
    "        \n",
    "    return total/i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a5c01837-2232-467c-b20c-5a39ae3e4404",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time for res= 0: 0.00 minutes.\n",
      "Time for res= 1: 0.00 minutes.\n",
      "Time for res= 2: 0.00 minutes.\n",
      "Time for res= 3: 0.01 minutes.\n",
      "Time for res= 4: 0.05 minutes.\n",
      "Time for res= 5: 0.39 minutes.\n",
      "Time for res= 6: 2.76 minutes.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{0: 1281.2560107413706,\n",
       " 1: 483.0568390741256,\n",
       " 2: 182.51295648919202,\n",
       " 3: 68.97922178773165,\n",
       " 4: 26.071759680163332,\n",
       " 5: 9.854090989974223,\n",
       " 6: 3.7245326671497363}"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max_res = 6\n",
    "d = {\n",
    "    res: avg_edge_len_at_res(res, unit='km')\n",
    "    for res in range(max_res+1)\n",
    "}\n",
    "d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d1651b57-9edd-4e45-ae9d-59dbfe24e20f",
   "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"
    }
   ],
   "source": [
    "x = list(d.keys())\n",
    "y = list(d.values())\n",
    "\n",
    "plt.semilogy(x, y, '-o')\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cfcc6aa5-5fd1-4dcc-a178-15825a699150",
   "metadata": {},
   "source": [
    "# todo: extrapolate values for finer resolutions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0e6528b3-baf0-46d3-a5a1-dc02ac732237",
   "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": 5
}