Orbit and Planes.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import math\n",
    "\n",
    "# #Default unit is km\n",
    "# earth_radius = 6378\n",
    "\n",
    "# plane_max_cruising_altitude = 13\n",
    "# plane_min_angle = math.radians(10) #rad\n",
    "\n",
    "\n",
    "# #Inputs\n",
    "# orbit_height = 1000\n",
    "\n",
    "\n",
    "# #Compute the radial distance between two reachable extremes in radians\n",
    "# rad = 2 * (math.pi/2 - plane_min_angle - math.asin(math.sin(math.pi/2 + plane_min_angle)*(earth_radius+plane_max_cruising_altitude)/(earth_radius+orbit_height)))\n",
    "\n",
    "# #Max length (diagonal) of a sector in radians\n",
    "# sector_max_length = rad / 5\n",
    "\n",
    "# #Max sector side length\n",
    "# sector_max_side = sector_max_length * math.sqrt(0.75) / 2\n",
    "\n",
    "# #sectors around the equator\n",
    "# sector_belt_count = math.ceil(2* math.pi / sector_max_side)\n",
    "\n",
    "# print(sector_belt_count)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Distinct Belts: 10\n",
      "Sector size efficiency: 0.9064017032397537\n",
      "Sectors per Belt: 18\n",
      "Total Satellites: 90\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "#Default unit is km\n",
    "earth_radius = 6378\n",
    "\n",
    "plane_max_cruising_altitude = 13\n",
    "plane_min_angle = math.radians(10) #rad\n",
    "\n",
    "\n",
    "#Inputs\n",
    "orbit_height = 20000\n",
    "\n",
    "\n",
    "#Compute the radial distance between two reachable extremes in radians\n",
    "rad = 2 * (math.pi/2 - plane_min_angle - math.asin(math.sin(math.pi/2 + plane_min_angle)*(earth_radius+plane_max_cruising_altitude)/(earth_radius+orbit_height)))\n",
    "\n",
    "#Max length (diagonal) of a sector in radians\n",
    "sector_max_length = rad / 5\n",
    "\n",
    "#Max horizontal spacing between two sectors\n",
    "sector_max_width = sector_max_length * 0.75\n",
    "\n",
    "#sectors around the equator\n",
    "sector_equator_count = math.ceil(math.pi / sector_max_width)\n",
    "\n",
    "#Determine actual sector size\n",
    "sector_width = math.pi / sector_equator_count\n",
    "sector_length = sector_width * 4/3\n",
    "\n",
    "#Diamater of inscribed circle (a.k.a. h)\n",
    "sector_h = sector_length * math.sqrt(0.75)\n",
    "\n",
    "#note the 2* (from 2*pi) outside of the ceil(). This guarantees an even Number.\n",
    "sector_belt_count = 2 * math.ceil(math.pi / sector_h)\n",
    "\n",
    "print(f\"Distinct Belts: {sector_equator_count}\")\n",
    "print(f\"Sector size efficiency: {sector_width/sector_max_width}\")\n",
    "print(f\"Sectors per Belt: {sector_belt_count}\")\n",
    "print(f\"Total Satellites: {sector_equator_count * sector_belt_count/2:.0f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Distinct Belts: 10\n",
      "Sector size efficiency: 0.9140708271677093\n",
      "Sectors per Belt: 18\n",
      "sector_h: 0.17453292519943295\n",
      "2 x sector_width:  0.6283185307179586\n",
      "Sector height efficiency: 0.4811252243246882\n",
      "Total Satellites: 90\n",
      "sector_max_width: 0.34369247548619\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "#Default unit is km\n",
    "earth_radius = 6378\n",
    "\n",
    "plane_max_cruising_altitude = 13\n",
    "plane_min_angle = math.radians(10) #rad\n",
    "\n",
    "\n",
    "#Inputs\n",
    "orbit_height = 19000\n",
    "\n",
    "\n",
    "#Compute the radial distance between two reachable extremes in radians\n",
    "rad = 2 * (math.pi/2 - plane_min_angle - math.asin(math.sin(math.pi/2 + plane_min_angle)*(earth_radius+plane_max_cruising_altitude)/(earth_radius+orbit_height)))\n",
    "\n",
    "#Max length (diagonal) of a sector in radians\n",
    "sector_max_length = rad / 5\n",
    "\n",
    "#Max horizontal spacing between two sectors\n",
    "sector_max_width = sector_max_length * 0.75\n",
    "\n",
    "#sectors around the equator\n",
    "sector_equator_count = math.ceil(math.pi / sector_max_width)\n",
    "\n",
    "#Determine actual sector size\n",
    "sector_width = math.pi / sector_equator_count\n",
    "sector_length = sector_width * 4/3\n",
    "\n",
    "#Diamater of inscribed circle (a.k.a. h)\n",
    "sector_max_h = sector_length * math.sqrt(0.75)\n",
    "\n",
    "#note the 6* (from 6*pi/3) outside of the ceil(). This guarantees a Number divisible by 6.\n",
    "sector_belt_count =  6*math.ceil(math.pi / (sector_max_h*3))\n",
    "\n",
    "sector_h =  math.pi / sector_belt_count\n",
    "\n",
    "print(f\"Distinct Belts: {sector_equator_count}\")\n",
    "print(f\"Sector size efficiency: {sector_width/sector_max_width}\")\n",
    "print(f\"Sectors per Belt: {sector_belt_count}\")\n",
    "print(\"sector_h:\", sector_h)\n",
    "y_radiant_per_belt = sector_h\n",
    "x_radiant_per_belt = 2*sector_width\n",
    "print(\"2 x sector_width: \", 2*sector_width)\n",
    "print(f\"Sector height efficiency: {sector_h/sector_max_h}\")\n",
    "print(f\"Total Satellites: {sector_equator_count * sector_belt_count/2:.0f}\")\n",
    "print(\"sector_max_width:\", sector_max_width)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SEC:  10\n",
      "[[0.         0.        ]\n",
      " [0.62831853 0.        ]\n",
      " [1.25663706 0.        ]\n",
      " [1.88495559 0.        ]\n",
      " [2.51327412 0.        ]\n",
      " [3.14159265 0.        ]]\n",
      "defaultdict(<function <lambda> at 0x00000135B2DCD5E8>, {'layer 0': array([[0.        , 0.        ],\n",
      "       [0.62831853, 0.        ],\n",
      "       [1.25663706, 0.        ],\n",
      "       [1.88495559, 0.        ],\n",
      "       [2.51327412, 0.        ]]), 'layer 1': array([[0.31415927, 0.17453293],\n",
      "       [0.9424778 , 0.17453293],\n",
      "       [1.57079633, 0.17453293],\n",
      "       [2.19911486, 0.17453293],\n",
      "       [2.82743339, 0.17453293]]), 'layer 2': array([[0.        , 0.34906585],\n",
      "       [0.62831853, 0.34906585],\n",
      "       [1.25663706, 0.34906585],\n",
      "       [1.88495559, 0.34906585],\n",
      "       [2.51327412, 0.34906585]]), 'layer 3': array([[0.31415927, 0.52359878],\n",
      "       [0.9424778 , 0.52359878],\n",
      "       [1.57079633, 0.52359878],\n",
      "       [2.19911486, 0.52359878],\n",
      "       [2.82743339, 0.52359878]]), 'layer 4': array([[0.        , 0.6981317 ],\n",
      "       [0.62831853, 0.6981317 ],\n",
      "       [1.25663706, 0.6981317 ],\n",
      "       [1.88495559, 0.6981317 ],\n",
      "       [2.51327412, 0.6981317 ]]), 'layer 5': array([[0.31415927, 0.87266463],\n",
      "       [0.9424778 , 0.87266463],\n",
      "       [1.57079633, 0.87266463],\n",
      "       [2.19911486, 0.87266463],\n",
      "       [2.82743339, 0.87266463]]), 'layer 6': array([[0.        , 1.04719755],\n",
      "       [0.62831853, 1.04719755],\n",
      "       [1.25663706, 1.04719755],\n",
      "       [1.88495559, 1.04719755],\n",
      "       [2.51327412, 1.04719755]]), 'layer 7': array([[0.31415927, 1.22173048],\n",
      "       [0.9424778 , 1.22173048],\n",
      "       [1.57079633, 1.22173048],\n",
      "       [2.19911486, 1.22173048],\n",
      "       [2.82743339, 1.22173048]]), 'layer 8': array([[0.        , 1.3962634 ],\n",
      "       [0.62831853, 1.3962634 ],\n",
      "       [1.25663706, 1.3962634 ],\n",
      "       [1.88495559, 1.3962634 ],\n",
      "       [2.51327412, 1.3962634 ]]), 'layer 9': array([[0.31415927, 1.57079633],\n",
      "       [0.9424778 , 1.57079633],\n",
      "       [1.57079633, 1.57079633],\n",
      "       [2.19911486, 1.57079633],\n",
      "       [2.82743339, 1.57079633]]), 'layer 10': array([[0.        , 1.74532925],\n",
      "       [0.62831853, 1.74532925],\n",
      "       [1.25663706, 1.74532925],\n",
      "       [1.88495559, 1.74532925],\n",
      "       [2.51327412, 1.74532925]]), 'layer 11': array([[0.31415927, 1.91986218],\n",
      "       [0.9424778 , 1.91986218],\n",
      "       [1.57079633, 1.91986218],\n",
      "       [2.19911486, 1.91986218],\n",
      "       [2.82743339, 1.91986218]]), 'layer 12': array([[0.        , 2.0943951 ],\n",
      "       [0.62831853, 2.0943951 ],\n",
      "       [1.25663706, 2.0943951 ],\n",
      "       [1.88495559, 2.0943951 ],\n",
      "       [2.51327412, 2.0943951 ]]), 'layer 13': array([[0.31415927, 2.26892803],\n",
      "       [0.9424778 , 2.26892803],\n",
      "       [1.57079633, 2.26892803],\n",
      "       [2.19911486, 2.26892803],\n",
      "       [2.82743339, 2.26892803]]), 'layer 14': array([[0.        , 2.44346095],\n",
      "       [0.62831853, 2.44346095],\n",
      "       [1.25663706, 2.44346095],\n",
      "       [1.88495559, 2.44346095],\n",
      "       [2.51327412, 2.44346095]]), 'layer 15': array([[0.31415927, 2.61799388],\n",
      "       [0.9424778 , 2.61799388],\n",
      "       [1.57079633, 2.61799388],\n",
      "       [2.19911486, 2.61799388],\n",
      "       [2.82743339, 2.61799388]]), 'layer 16': array([[0.        , 2.7925268 ],\n",
      "       [0.62831853, 2.7925268 ],\n",
      "       [1.25663706, 2.7925268 ],\n",
      "       [1.88495559, 2.7925268 ],\n",
      "       [2.51327412, 2.7925268 ]]), 'layer 17': array([[0.31415927, 2.96705973],\n",
      "       [0.9424778 , 2.96705973],\n",
      "       [1.57079633, 2.96705973],\n",
      "       [2.19911486, 2.96705973],\n",
      "       [2.82743339, 2.96705973]])})\n",
      "(5, 2)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\kuoyi\\anaconda3\\lib\\site-packages\\ipykernel_launcher.py:43: FutureWarning: arrays to stack must be passed as a \"sequence\" type such as list or tuple. Support for non-sequence iterables such as generators is deprecated as of NumPy 1.16 and will raise an error in the future.\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "def cell(left, right):\n",
    "    cell_center = np.array([left, right])\n",
    "    return cell_center\n",
    "\n",
    "def cell_corners(cell_center):\n",
    "    cell_center\n",
    "    return cell_corners\n",
    "\n",
    "# Alpha Cell\n",
    "alpha = np.array([0,0]) \n",
    "beta = np.array([0,0]) \n",
    "print(\"SEC: \", sector_equator_count)\n",
    "#number_belt= sector_equator_count/2\n",
    "list_position = [[0,0]]\n",
    "for i in range(int(sector_equator_count/2.0)):\n",
    "    beta = np.add(beta, np.array([2*sector_width, 0]))\n",
    "    #print(\"Beta: \", beta)\n",
    "    list_position= np.append(list_position, [beta] , axis=0)\n",
    "    #print(\"Alpha:\", alpha)\n",
    "    ##list_position = np.append(alpha, beta, axis=0)\n",
    "    #print(\"Beta: \", beta)\n",
    "    alpha = beta\n",
    "    #list_position = list_position[0]\n",
    "print(list_position)\n",
    "\n",
    "from collections import defaultdict\n",
    "mean_coordinates = []\n",
    "mean_coordinates_dict = defaultdict(lambda:np.empty((0,2),float))\n",
    "for y_belt_count in range(int(sector_belt_count)):\n",
    "#     for x_belt_count in range(int(sector_equator_count/2.0)):\n",
    "# #         beta = np.add(beta, np.array([2*sector_width, 0]))\n",
    "# #         list_position= np.append(list_position, [beta] , axis=0)\n",
    "# #         alpha = beta\n",
    "#         x_radiant = (x_belt_count +(y_belt_count%2)) * x_radiant_per_belt \n",
    "#         y_radiant = y_belt_count * y_radiant_per_belt \n",
    "#         mean_coordinates.append([x_radiant, y_radiant])\n",
    "# #         mean_coordinates_dict[f\"layer {y_belt_count}\"].append([x_radiant, y_radiant])\n",
    "#         np.hstack((mean_coordinates_dict[f\"layer {y_belt_count}\"],[x_radiant, y_radiant]))\n",
    "        mean_coordinates_dict[f\"layer {y_belt_count}\"] = np.vstack([[(x_belt_count +(y_belt_count%2)/2) * x_radiant_per_belt,\n",
    "                                                                    y_belt_count * y_radiant_per_belt]] \n",
    "                                                                   for x_belt_count in range(int(sector_equator_count/2.0)))\n",
    "\n",
    "\n",
    "    \n",
    "\n",
    "#print(2*sector_max_width)\n",
    "print(mean_coordinates_dict)\n",
    "print(mean_coordinates_dict[\"layer 0\"].shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import pairwise_distances\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "smaller within [[ True False False False False]\n",
      " [False  True False False False]\n",
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      " [False False False  True False]\n",
      " [False False False False  True]]\n",
      "to delete []\n",
      "smaller [[False False False False False]\n",
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      " [False False False False False]]\n",
      "shpae before (5, 2) delete []\n",
      "shpae after (5, 2)\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller within [[ True False False False False]\n",
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      "to delete []\n",
      "smaller [[False False False False False]\n",
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      "shpae before (5, 2) delete []\n",
      "shpae after (5, 2)\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller within [[ True False False False False]\n",
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      "to delete []\n",
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      "shpae before (5, 2) delete []\n",
      "shpae after (5, 2)\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller within [[ True False False False False]\n",
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      "to delete []\n",
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      "shpae before (5, 2) delete []\n",
      "shpae after (5, 2)\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller within [[ True False False False False]\n",
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      "to delete []\n",
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      " [False False False False False]]\n",
      "shpae before (5, 2) delete []\n",
      "shpae after (5, 2)\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller within [[ True False False False False]\n",
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      "to delete []\n",
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      "shpae before (5, 2) delete []\n",
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      "smaller within []\n",
      "to delete []\n",
      "smaller within [[ True False False False False]\n",
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      "to delete []\n",
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      " [False False False False False]]\n",
      "shpae before (5, 2) delete []\n",
      "shpae after (5, 2)\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller within [[ True False False False False]\n",
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      "to delete []\n",
      "smaller [[False False False False False]\n",
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      "shpae before (5, 2) delete []\n",
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      "smaller within []\n",
      "to delete []\n",
      "smaller within [[ True False False False False]\n",
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      "to delete []\n",
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      "shpae before (5, 2) delete []\n",
      "shpae after (5, 2)\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller within [[ True False False False False]\n",
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      "to delete []\n",
      "smaller [[False False False False False]\n",
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      " [False False False False False]]\n",
      "shpae before (5, 2) delete []\n",
      "shpae after (5, 2)\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller within [[ True False False False False]\n",
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      "to delete []\n",
      "smaller [[False False False False False]\n",
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      " [False False False False False]]\n",
      "shpae before (5, 2) delete []\n",
      "shpae after (5, 2)\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller within [[ True False False False False]\n",
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      "to delete []\n",
      "smaller [[False False False False False]\n",
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      " [False False False False False]]\n",
      "shpae before (5, 2) delete []\n",
      "shpae after (5, 2)\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller within [[ True False False False False]\n",
      " [False  True False False False]\n",
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      " [False False False  True False]\n",
      " [False False False False  True]]\n",
      "to delete []\n",
      "smaller [[False False False False False]\n",
      " [False False False False False]\n",
      " [False False False False False]\n",
      " [False False False False False]\n",
      " [False False False False False]]\n",
      "shpae before (5, 2) delete []\n",
      "shpae after (5, 2)\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller within [[ True False False False False]\n",
      " [False  True False False False]\n",
      " [False False  True False False]\n",
      " [False False False  True False]\n",
      " [False False False False  True]]\n",
      "to delete []\n",
      "smaller [[False False False False False]\n",
      " [False False False False False]\n",
      " [False False False False False]\n",
      " [False False False False False]\n",
      " [False False False False False]]\n",
      "shpae before (5, 2) delete []\n",
      "shpae after (5, 2)\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller within [[ True False False False False]\n",
      " [False  True False False False]\n",
      " [False False  True False False]\n",
      " [False False False  True False]\n",
      " [False False False False  True]]\n",
      "to delete []\n",
      "smaller [[False False False False False]\n",
      " [False False False False False]\n",
      " [False False False False False]\n",
      " [False False False False False]\n",
      " [False False False False False]]\n",
      "shpae before (5, 2) delete []\n",
      "shpae after (5, 2)\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller within [[ True False False False False]\n",
      " [False  True False False False]\n",
      " [False False  True False False]\n",
      " [False False False  True False]\n",
      " [False False False False  True]]\n",
      "to delete []\n",
      "smaller [[False False False False False]\n",
      " [False False False False False]\n",
      " [False False False False False]\n",
      " [False False False False False]\n",
      " [False False False False False]]\n",
      "shpae before (5, 2) delete []\n",
      "shpae after (5, 2)\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller within [[ True False False False False]\n",
      " [False  True False False False]\n",
      " [False False  True False False]\n",
      " [False False False  True False]\n",
      " [False False False False  True]]\n",
      "to delete []\n",
      "smaller [[False False False False False]\n",
      " [False False False False False]\n",
      " [False False False False False]\n",
      " [False False False False False]\n",
      " [False False False False False]]\n",
      "shpae before (5, 2) delete []\n",
      "shpae after (5, 2)\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller within [[ True False False False False]\n",
      " [False  True False False False]\n",
      " [False False  True False False]\n",
      " [False False False  True False]\n",
      " [False False False False  True]]\n",
      "to delete []\n",
      "smaller []\n",
      "shpae before (0, 2) delete []\n",
      "shpae after (0, 2)\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller []\n",
      "shpae before (0, 2) delete []\n",
      "shpae after (0, 2)\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller []\n",
      "shpae before (0, 2) delete []\n",
      "shpae after (0, 2)\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller []\n",
      "shpae before (0, 2) delete []\n",
      "shpae after (0, 2)\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller []\n",
      "shpae before (0, 2) delete []\n",
      "shpae after (0, 2)\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller []\n",
      "shpae before (0, 2) delete []\n",
      "shpae after (0, 2)\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller []\n",
      "shpae before (0, 2) delete []\n",
      "shpae after (0, 2)\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller []\n",
      "shpae before (0, 2) delete []\n",
      "shpae after (0, 2)\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller []\n",
      "shpae before (0, 2) delete []\n",
      "shpae after (0, 2)\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller []\n",
      "shpae before (0, 2) delete []\n",
      "shpae after (0, 2)\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller []\n",
      "shpae before (0, 2) delete []\n",
      "shpae after (0, 2)\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller []\n",
      "shpae before (0, 2) delete []\n",
      "shpae after (0, 2)\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller []\n",
      "shpae before (0, 2) delete []\n",
      "shpae after (0, 2)\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller []\n",
      "shpae before (0, 2) delete []\n",
      "shpae after (0, 2)\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller []\n",
      "shpae before (0, 2) delete []\n",
      "shpae after (0, 2)\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller []\n",
      "shpae before (0, 2) delete []\n",
      "shpae after (0, 2)\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller []\n",
      "shpae before (0, 2) delete []\n",
      "shpae after (0, 2)\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller within []\n",
      "to delete []\n",
      "smaller []\n",
      "shpae before (0, 2) delete []\n",
      "shpae after (0, 2)\n",
      "smaller within []\n",
      "to delete []\n",
      "pw_distances:  []\n"
     ]
    }
   ],
   "source": [
    "#remove the overlapping centroids \n",
    "def delete_within_belt(y_belt):\n",
    "    #y_belt is the layer to delete in\n",
    "    #in order for this to work we need mean_coordinates_dict as a global dict\n",
    "    within_belt_distances = pairwise_distances(mean_coordinates_dict[f\"layer {y_belt}\"], mean_coordinates_dict[f\"layer {y_belt}\"],metric='haversine')\n",
    "    to_delete=[]\n",
    "    for row_idx,row in enumerate(within_belt_distances):\n",
    "        for col, element in enumerate(row):\n",
    "            if element < y_radiant_per_belt and row_idx!=col:\n",
    "                to_delete.append(col)\n",
    "    print(\"smaller within\", within_belt_distances<y_radiant_per_belt)\n",
    "    print(f\"to delete {to_delete}\")\n",
    "    mean_coordinates_dict[f\"layer {y_belt}\"] = np.delete(mean_coordinates_dict[f\"layer {y_belt}\"], to_delete, 0)\n",
    "    \n",
    "\n",
    "\n",
    "for y_belt in range(sector_belt_count*2-1):\n",
    "    #within the current belt\n",
    "#     within_belt_distances = pairwise_distances(mean_coordinates_dict[f\"layer {y_belt}\"], mean_coordinates_dict[f\"layer {y_belt}\"],metric='haversine')\n",
    "#     to_delete=[]\n",
    "#     for row_idx,row in enumerate(within_belt_distances):\n",
    "#         for col, element in enumerate(row):\n",
    "#             if element < y_radiant_per_belt and row_idx!=col:\n",
    "#                 to_delete.append(col)\n",
    "#     print(\"smaller within\", within_belt_distances<y_radiant_per_belt)\n",
    "#     print(f\"to delete {to_delete}\")\n",
    "#     mean_coordinates_dict[f\"layer {y_belt}\"] = np.delete(mean_coordinates_dict[f\"layer {y_belt}\"], to_delete, 0)\n",
    "    delete_within_belt(y_belt)\n",
    "    \n",
    "    \n",
    "    # inside out, thus in neighboring belts\n",
    "    pw_distances = pairwise_distances(mean_coordinates_dict[f\"layer {y_belt}\"], mean_coordinates_dict[f\"layer {y_belt+1}\"],metric='haversine')\n",
    "    #print(f\"layer {y_belt} {pw_distances}\")\n",
    "    print(\"smaller\", pw_distances<y_radiant_per_belt)\n",
    "    to_delete=[]\n",
    "    for row in pw_distances:\n",
    "        for col, element in enumerate(row):\n",
    "            if element < y_radiant_per_belt:\n",
    "                #mean_coordinates_dict[f\"layer {y_belt+1}\"]= np.delete(mean_coordinates_dict[f\"layer {y_belt+1}\"], col, 0)\n",
    "                to_delete.append(col)            \n",
    "    print('shpae before', mean_coordinates_dict[f\"layer {y_belt+1}\"].shape, 'delete', to_delete)\n",
    "    mean_coordinates_dict[f\"layer {y_belt+1}\"]= np.delete(mean_coordinates_dict[f\"layer {y_belt+1}\"], to_delete, 0)#print(point.shape)\n",
    "    print('shpae after', mean_coordinates_dict[f\"layer {y_belt+1}\"].shape)\n",
    "    \n",
    "    \n",
    "    #also delete in the final ball\n",
    "    y_belt =sector_belt_count*2\n",
    "    delete_within_belt(y_belt)\n",
    "print(\"pw_distances: \", pw_distances)\n",
    "# for centroid in mean_coordinates_dict[f\"layer {1}\"]:\n",
    "#print(pairwise_distances(mean_coordinates_dict[\"layer 1\"], mean_coordinates_dict[\"layer 1\"], metric='haversine'))\n",
    "#print(mean_coordinates_dict)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape (37, 2)\n",
      "Dim True_Data: (90, 2)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\kuoyi\\anaconda3\\lib\\site-packages\\ipykernel_launcher.py:4: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray.\n",
      "  after removing the cwd from sys.path.\n"
     ]
    }
   ],
   "source": [
    "result = mean_coordinates_dict.items()\n",
    "#print('val shape', mean_coordinates_dict.values())\n",
    "data = list(result)\n",
    "numpyArray = np.array(data)\n",
    "#print(numpyArray)\n",
    "\n",
    "true_data_array = np.vstack([x for x in numpyArray[:,1]])\n",
    "print(\"Shape\",numpyArray.shape)\n",
    "#np.concatenate((true_data_array[0], true_data_array[1], true_data_array[2], true_data_array[3]), 1)\n",
    "#true_data_array= np.concatenate((true_data_array[0], true_data_array[1], true_data_array[2], true_data_array[3]), 0)\n",
    "\n",
    "\n",
    "#print('testo',np.hstack([x for x in mean_coordinates_dict.keys()]).shape)\n",
    "#print(\"true:\", true_data_array)\n",
    "print(\"Dim True_Data:\", true_data_array.shape)\n",
    "\n",
    "\n",
    "# import pdb\n",
    "# test = np.hstack((true_data_array[:,0],-true_data_array[:,1]))\n",
    "# pdb.set_trace()\n",
    "\n",
    "earth_array = np.vstack((true_data_array, \n",
    "                         -true_data_array,\n",
    "                         np.vstack((true_data_array[:,0],-true_data_array[:,1])).T,\n",
    "                         np.vstack((-true_data_array[:,0],true_data_array[:,1])).T\n",
    "))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import numpy as np\n",
    "# import freud\n",
    "# import matplotlib\n",
    "# import matplotlib.pyplot as plt\n",
    "\n",
    "# points = earth_array\n",
    "# plt.scatter(points[:,0], points[:,1])\n",
    "# plt.title('Points')\n",
    "# plt.xlim((-1, math.pi))\n",
    "# plt.ylim((-1, math.pi))\n",
    "# plt.show()\n",
    "\n",
    "# # We must add a z=0 component to this array for freud\n",
    "# points = np.hstack((points, np.zeros((points.shape[0], 1))))\n",
    "\n",
    "# L = 2\n",
    "# box = freud.box.Box.square(L)\n",
    "# voro = freud.voronoi.Voronoi(box, L/2)\n",
    "\n",
    "\n",
    "# cells = voro.compute(box=box, positions=points).polytopes\n",
    "# print(cells)\n",
    "\n",
    "\n",
    "# def draw_voronoi(box, points, cells, nlist=None, color_by_sides=False):\n",
    "#     ax = plt.gca()\n",
    "#     # Draw Voronoi cells\n",
    "#     patches = [plt.Polygon(cell[:, :2]) for cell in cells]\n",
    "#     patch_collection = matplotlib.collections.PatchCollection(patches, edgecolors='black', alpha=0.4)\n",
    "#     cmap = plt.cm.viridis\n",
    "#     if color_by_sides:\n",
    "#         colors = [len(cell) for cell in voro.polytopes]\n",
    "#     else:\n",
    "#         colors = np.random.permutation(np.arange(len(patches)))\n",
    "#     patch_collection.set_array(np.array(colors))\n",
    "#     ax.add_collection(patch_collection)\n",
    "\n",
    "#     # Draw points\n",
    "#     plt.scatter(points[:,0], points[:,1], c=colors)\n",
    "#     plt.title('Voronoi Diagram')\n",
    "#     plt.xlim((-box.Lx/2, box.Lx/2))\n",
    "#     plt.ylim((-box.Ly/2, box.Ly/2))\n",
    "\n",
    "#     # Set equal aspect and draw box\n",
    "#     ax.set_aspect('equal', 'datalim')\n",
    "#     box_patch = plt.Rectangle([-box.Lx/2, -box.Ly/2], box.Lx, box.Ly, alpha=1, fill=None)\n",
    "#     ax.add_patch(box_patch)\n",
    "\n",
    "#     # Draw neighbor lines\n",
    "#     if nlist is not None:\n",
    "#         bonds = np.asarray([points[j] - points[i] for i, j in zip(nlist.index_i, nlist.index_j)])\n",
    "#         box.wrap(bonds)\n",
    "#         line_data = np.asarray([[points[nlist.index_i[i]],\n",
    "#                                  points[nlist.index_i[i]]+bonds[i]] for i in range(len(nlist.index_i))])\n",
    "#         line_data = line_data[:, :, :2]\n",
    "#         line_collection = matplotlib.collections.LineCollection(line_data, alpha=0.3)\n",
    "#         ax.add_collection(line_collection)\n",
    "\n",
    "#     # Show colorbar for number of sides\n",
    "#     if color_by_sides:\n",
    "#         plt.colorbar()\n",
    "#     plt.show()\n",
    "\n",
    "# draw_voronoi(box, points, voro.polytopes)\n",
    "\n",
    "# def hexagonal_lattice(rows=3, cols=3, noise=0):\n",
    "#     # Assemble a hexagonal lattice\n",
    "#     points = []\n",
    "#     for row in range(rows*2):\n",
    "#         for col in range(cols):\n",
    "#             x = (col + (0.5 * (row % 2)))*np.sqrt(3)\n",
    "#             y = row*0.5\n",
    "#             points.append((x, y, 0))\n",
    "#     points = np.asarray(true_data_array)\n",
    "#     points += np.random.multivariate_normal(mean=np.zeros(3), cov=np.eye(3)*noise, size=points.shape[0])\n",
    "#     # Set z=0 again for all points after adding Gaussian noise\n",
    "#     points[:, 2] = 0\n",
    "\n",
    "#     # Wrap the points into the box\n",
    "#     box = freud.box.Box(Lx=cols*np.sqrt(3), Ly=rows, is2D=True)\n",
    "#     points = box.wrap(points)\n",
    "#     return box, points\n",
    "\n",
    "# # Compute the Voronoi diagram and plot\n",
    "# box, points = hexagonal_lattice()\n",
    "# voro = freud.voronoi.Voronoi(box, np.max(box.L)/2)\n",
    "# voro.compute(box=box, positions=true_data_array)\n",
    "# draw_voronoi(box, points, voro.polytopes)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      "Bad key \"text.kerning_factor\" on line 4 in\n",
      "C:\\Users\\kuoyi\\anaconda3\\lib\\site-packages\\matplotlib\\mpl-data\\stylelib\\_classic_test_patch.mplstyle.\n",
      "You probably need to get an updated matplotlibrc file from\n",
      "https://github.com/matplotlib/matplotlib/blob/v3.1.3/matplotlibrc.template\n",
      "or from the matplotlib source distribution\n"
     ]
    },
    {
     "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": [
    "from scipy.spatial import Voronoi, voronoi_plot_2d\n",
    "points = earth_array\n",
    "vor = Voronoi(points)\n",
    "import matplotlib.pyplot as plt\n",
    "fig = voronoi_plot_2d(vor)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Vertices:  (612, 2)\n",
      "indices of voronoi vertices forming voroni ridges [[10, 11], [11, 18], [8, 9], [9, 10], [8, 17], [17, 18], [12, 13], [13, 42], [20, 21], [12, 21], [20, 41], [41, 42], [18, 64], [21, 63], [11, 12], [63, 64], [55, 59], [17, 55], [59, 65], [64, 65], [56, 58], [56, 66], [57, 59], [57, 58], [65, 66], [76, 78], [25, 76], [25, 26], [26, 80], [78, 80], [27, 85], [27, 91], [85, 88], [88, 92], [91, 92], [86, 87], [86, 93], [88, 89], [87, 89], [92, 93], [94, 97], [94, 95], [95, 96], [96, 98], [97, 98], [90, 93], [90, 96], [91, 95], [69, 70], [70, 98], [28, 90], [28, 69], [-1, 103], [-1, 30], [30, 31], [31, 103], [-1, 77], [-1, 76], [77, 78], [-1, 37], [-1, 39], [37, 40], [39, 40], [-1, 32], [30, 33], [32, 33], [-1, 99], [-1, 29], [29, 101], [99, 101], [37, 100], [99, 100], [-1, 24], [-1, 3], [3, 4], [4, 24], [105, 110], [105, 106], [106, 107], [107, 109], [108, 109], [108, 110], [35, 36], [33, 36], [32, 110], [35, 105], [-1, 108], [24, 109], [100, 115], [101, 102], [102, 114], [114, 115], [34, 106], [34, 118], [35, 119], [118, 119], [-1, 25], [-1, 94], [-1, 27], [45, 46], [46, 47], [1, 45], [1, 128], [47, 129], [128, 129], [137, 140], [137, 139], [138, 139], [138, 141], [140, 142], [141, 142], [13, 137], [10, 140], [52, 138], [14, 52], [48, 141], [15, 48], [14, 15], [6, 9], [6, 50], [50, 142], [49, 51], [48, 51], [49, 50], [44, 46], [43, 44], [43, 146], [45, 145], [145, 146], [41, 43], [20, 67], [67, 147], [146, 147], [148, 151], [148, 150], [149, 150], [149, 152], [151, 153], [152, 153], [67, 149], [63, 152], [56, 60], [66, 153], [60, 61], [61, 151], [70, 71], [71, 72], [72, 165], [69, 167], [165, 167], [-1, 168], [97, 169], [168, 169], [71, 170], [169, 170], [168, 171], [170, 172], [171, 172], [-1, 2], [-1, 173], [2, 174], [173, 174], [178, 183], [178, 180], [179, 180], [179, 182], [181, 183], [181, 182], [184, 188], [184, 186], [185, 186], [185, 187], [187, 188], [-1, 184], [171, 186], [189, 193], [189, 190], [190, 191], [191, 192], [192, 193], [75, 180], [74, 75], [74, 193], [179, 189], [188, 190], [182, 187], [-1, 191], [26, 192], [79, 80], [74, 79], [197, 199], [197, 198], [198, 200], [199, 202], [200, 201], [201, 202], [-1, 197], [77, 199], [2, 198], [79, 202], [73, 75], [73, 201], [89, 204], [81, 82], [82, 203], [81, 87], [203, 204], [-1, 205], [103, 207], [205, 207], [29, 206], [205, 206], [112, 113], [113, 164], [163, 164], [112, 216], [163, 217], [216, 217], [31, 223], [36, 222], [222, 223], [207, 208], [208, 224], [223, 224], [111, 112], [117, 226], [111, 117], [216, 228], [226, 228], [83, 84], [84, 235], [81, 236], [82, 83], [235, 236], [125, 126], [126, 242], [241, 244], [125, 241], [242, 244], [-1, 247], [-1, 125], [126, 246], [246, 247], [5, 84], [5, 248], [83, 127], [127, 249], [248, 249], [245, 247], [245, 253], [246, 252], [252, 253], [-1, 243], [-1, 241], [243, 244], [-1, 57], [-1, 55], [-1, 143], [-1, 16], [16, 53], [53, 143], [-1, 49], [-1, 7], [7, 51], [-1, 6], [-1, 8], [-1, 54], [54, 58], [132, 135], [132, 133], [135, 136], [136, 259], [133, 261], [259, 261], [47, 134], [129, 260], [134, 136], [259, 260], [158, 159], [131, 159], [130, 131], [130, 266], [158, 263], [263, 266], [132, 156], [156, 158], [135, 264], [263, 264], [68, 130], [14, 68], [52, 265], [265, 266], [-1, 267], [16, 268], [267, 268], [275, 277], [275, 276], [276, 278], [277, 279], [278, 280], [279, 280], [-1, 275], [143, 277], [7, 276], [15, 278], [154, 280], [68, 154], [1, 22], [145, 281], [22, 282], [281, 282], [230, 231], [23, 231], [22, 23], [230, 283], [282, 283], [122, 232], [120, 122], [120, 284], [230, 232], [283, 284], [53, 285], [279, 286], [285, 286], [155, 289], [155, 271], [271, 274], [274, 287], [287, 289], [165, 166], [166, 292], [167, 234], [234, 294], [292, 294], [200, 296], [174, 298], [296, 298], [300, 301], [300, 302], [301, 305], [302, 303], [303, 304], [304, 305], [-1, 300], [3, 301], [173, 302], [297, 298], [297, 303], [175, 304], [175, 176], [297, 299], [176, 299], [209, 212], [175, 212], [176, 307], [209, 306], [306, 307], [73, 309], [178, 308], [308, 309], [296, 311], [309, 311], [299, 310], [310, 311], [312, 316], [312, 313], [313, 314], [314, 317], [315, 317], [315, 316], [172, 312], [185, 316], [72, 313], [194, 314], [166, 194], [183, 195], [195, 196], [196, 317], [181, 315], [318, 322], [318, 319], [319, 320], [320, 321], [321, 322], [-1, 320], [245, 319], [85, 321], [204, 322], [203, 325], [127, 323], [323, 325], [318, 324], [324, 325], [253, 326], [324, 326], [327, 329], [327, 331], [328, 329], [328, 332], [330, 331], [330, 332], [102, 327], [206, 329], [208, 328], [116, 332], [116, 225], [224, 225], [333, 335], [333, 338], [334, 335], [334, 336], [336, 337], [337, 338], [34, 104], [104, 333], [107, 338], [209, 210], [210, 211], [211, 335], [212, 334], [305, 336], [4, 337], [38, 341], [38, 39], [40, 340], [340, 341], [115, 342], [340, 342], [114, 344], [331, 343], [343, 344], [339, 342], [339, 345], [344, 345], [351, 352], [351, 353], [352, 354], [353, 356], [354, 355], [355, 356], [162, 163], [217, 354], [213, 352], [162, 213], [218, 219], [218, 220], [219, 353], [220, 221], [221, 356], [227, 228], [227, 355], [116, 357], [229, 358], [229, 330], [357, 358], [222, 361], [119, 360], [360, 361], [225, 362], [361, 362], [366, 369], [366, 368], [367, 368], [367, 370], [369, 371], [370, 371], [28, 366], [86, 369], [234, 368], [293, 294], [233, 367], [233, 293], [236, 371], [372, 375], [372, 373], [373, 374], [374, 377], [375, 376], [376, 377], [122, 123], [123, 375], [120, 121], [121, 372], [0, 373], [0, 19], [62, 121], [19, 62], [0, 5], [235, 374], [370, 377], [124, 376], [124, 233], [237, 238], [113, 237], [164, 382], [238, 384], [382, 384], [378, 379], [239, 379], [238, 239], [378, 383], [383, 384], [104, 386], [211, 387], [386, 387], [237, 389], [239, 240], [240, 391], [389, 391], [111, 390], [389, 390], [392, 393], [392, 395], [393, 394], [394, 397], [395, 396], [396, 397], [61, 144], [144, 393], [148, 392], [144, 256], [251, 394], [251, 255], [255, 256], [248, 397], [249, 250], [250, 251], [19, 396], [242, 398], [252, 399], [398, 399], [-1, 400], [-1, 254], [254, 402], [400, 402], [243, 401], [400, 401], [398, 403], [401, 403], [404, 406], [404, 408], [405, 406], [405, 409], [407, 408], [407, 409], [60, 404], [256, 406], [54, 408], [-1, 407], [254, 409], [410, 415], [410, 411], [411, 412], [412, 414], [413, 414], [413, 415], [258, 412], [133, 258], [156, 414], [157, 159], [157, 413], [382, 418], [162, 417], [417, 418], [383, 385], [385, 419], [418, 419], [420, 422], [420, 424], [421, 422], [421, 425], [423, 424], [423, 425], [257, 258], [261, 422], [257, 420], [260, 262], [262, 421], [213, 423], [214, 351], [214, 424], [416, 417], [416, 425], [426, 428], [426, 427], [427, 429], [428, 431], [429, 430], [430, 431], [139, 426], [265, 428], [42, 427], [44, 429], [264, 431], [134, 430], [432, 433], [432, 434], [433, 435], [434, 436], [435, 436], [-1, 432], [267, 433], [437, 439], [437, 441], [438, 439], [438, 442], [440, 442], [440, 441], [62, 437], [284, 439], [395, 441], [281, 438], [147, 442], [150, 440], [154, 443], [286, 444], [443, 444], [131, 445], [443, 445], [446, 450], [446, 448], [447, 448], [447, 449], [449, 451], [450, 451], [161, 410], [161, 446], [291, 415], [291, 450], [349, 350], [161, 350], [288, 448], [288, 349], [289, 290], [288, 290], [287, 447], [273, 274], [160, 449], [160, 273], [194, 452], [196, 453], [452, 453], [292, 456], [452, 459], [456, 459], [455, 458], [454, 455], [453, 454], [458, 459], [177, 210], [306, 461], [177, 460], [460, 461], [464, 466], [464, 465], [465, 467], [466, 469], [467, 468], [468, 469], [454, 464], [195, 466], [455, 463], [462, 463], [462, 465], [307, 467], [461, 462], [308, 469], [310, 468], [470, 473], [470, 471], [471, 472], [472, 474], [473, 475], [474, 475], [463, 474], [457, 458], [457, 472], [460, 475], [323, 478], [250, 476], [476, 478], [326, 477], [477, 478], [399, 479], [477, 479], [339, 482], [341, 481], [481, 482], [489, 490], [489, 491], [490, 492], [491, 494], [492, 493], [493, 494], [257, 490], [411, 489], [350, 491], [214, 492], [347, 349], [347, 348], [348, 494], [219, 493], [215, 218], [215, 348], [495, 499], [495, 496], [496, 497], [497, 498], [498, 500], [499, 500], [117, 496], [388, 390], [388, 495], [362, 500], [357, 498], [359, 499], [359, 360], [343, 503], [229, 502], [502, 503], [345, 346], [346, 504], [503, 504], [227, 508], [221, 506], [506, 508], [231, 364], [232, 509], [364, 510], [509, 510], [511, 516], [511, 513], [512, 513], [512, 514], [514, 515], [515, 516], [295, 511], [295, 471], [381, 513], [381, 470], [378, 512], [380, 381], [379, 380], [365, 385], [365, 514], [363, 364], [363, 365], [510, 515], [517, 522], [517, 519], [518, 519], [518, 521], [520, 522], [520, 521], [177, 517], [473, 522], [387, 519], [380, 520], [240, 521], [523, 528], [523, 524], [524, 525], [525, 526], [526, 527], [527, 528], [388, 528], [359, 523], [118, 524], [386, 525], [518, 526], [391, 527], [529, 532], [529, 531], [530, 531], [530, 533], [532, 534], [533, 534], [255, 532], [405, 529], [402, 531], [403, 530], [479, 533], [476, 534], [535, 539], [535, 537], [536, 537], [536, 540], [538, 540], [538, 539], [23, 539], [363, 535], [419, 537], [416, 536], [262, 540], [128, 538], [457, 544], [295, 542], [542, 544], [456, 543], [543, 544], [293, 545], [543, 545], [482, 548], [346, 546], [546, 548], [480, 547], [480, 481], [547, 548], [501, 551], [501, 502], [504, 550], [550, 551], [554, 557], [554, 556], [555, 556], [555, 558], [557, 559], [558, 559], [506, 507], [507, 554], [220, 557], [552, 553], [505, 553], [505, 507], [552, 556], [215, 486], [486, 559], [486, 560], [347, 561], [560, 561], [290, 562], [561, 562], [563, 565], [563, 566], [564, 565], [564, 568], [566, 567], [567, 568], [226, 563], [508, 565], [497, 566], [505, 564], [551, 553], [501, 568], [358, 567], [569, 571], [569, 570], [570, 574], [571, 572], [572, 573], [573, 574], [123, 569], [509, 571], [124, 570], [545, 574], [516, 572], [542, 573], [269, 436], [541, 575], [269, 541], [435, 576], [575, 576], [268, 577], [576, 577], [285, 578], [577, 578], [157, 580], [445, 579], [579, 580], [291, 581], [580, 581], [269, 270], [270, 582], [541, 583], [582, 583], [160, 585], [272, 273], [272, 584], [584, 585], [586, 589], [586, 587], [587, 588], [588, 591], [589, 590], [590, 591], [483, 549], [483, 484], [484, 586], [549, 589], [484, 487], [487, 488], [485, 488], [485, 587], [552, 588], [485, 555], [550, 591], [546, 590], [547, 549], [558, 593], [560, 592], [592, 593], [488, 594], [593, 594], [444, 596], [579, 595], [595, 596], [578, 598], [596, 598], [575, 597], [597, 598], [599, 603], [599, 600], [600, 601], [601, 602], [602, 604], [603, 604], [595, 603], [581, 599], [451, 600], [585, 601], [582, 584], [583, 602], [597, 604], [562, 607], [592, 605], [605, 607], [155, 606], [606, 607], [-1, 608], [-1, 609], [608, 610], [609, 611], [610, 611], [-1, 483], [487, 608], [-1, 271], [606, 609], [594, 610], [605, 611], [-1, 480], [-1, 272], [-1, 270], [-1, 434], [-1, 38]]\n"
     ]
    }
   ],
   "source": [
    "print (\"Vertices: \",vor.vertices.shape)\n",
    "#print (\"Vertices: \",vor.vertices)\n",
    "print(f\"indices of voronoi vertices forming voroni ridges {vor.ridge_vertices}\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--\n",
      "[[537, 419, 385, 365, 363, 535], [384, 238, 239, 379, 378, 383], [527, 391, 240, 521, 518, 526], [525, 386, 104, 34, 118, 524], [110, 105, 106, 107, 109, 108], [419, 385, 383, 384, 382, 418], [391, 240, 239, 238, 237, 389], [528, 523, 524, 525, 526, 527], [119, 35, 105, 106, 34, 118], [108, 613, 612, 32, 110], [537, 419, 418, 417, 416, 536], [384, 238, 237, 113, 164, 382], [528, 388, 390, 389, 391, 527], [524, 118, 119, 360, 359, 523], [110, 32, 33, 36, 35, 105], [418, 382, 164, 163, 162, 417], [390, 111, 112, 113, 237, 389], [528, 388, 495, 499, 359, 523], [361, 222, 36, 35, 119, 360], [33, 32, 615, 614, 30], [425, 416, 417, 162, 213, 423], [217, 163, 164, 113, 112, 216], [496, 117, 111, 390, 388, 495], [500, 362, 361, 360, 359, 499], [223, 31, 30, 33, 36, 222], [354, 217, 163, 162, 213, 352], [228, 216, 112, 111, 117, 226], [500, 498, 497, 496, 495, 499], [362, 225, 224, 223, 222, 361], [30, 617, 616, 103, 31], [424, 214, 351, 352, 213, 423], [355, 227, 228, 216, 217, 354], [566, 497, 496, 117, 226, 563], [500, 362, 225, 116, 357, 498], [224, 208, 207, 103, 31, 223], [356, 353, 351, 352, 354, 355], [565, 508, 227, 228, 226, 563], [567, 358, 357, 498, 497, 566], [332, 116, 225, 224, 208, 328], [103, 618, 619, 205, 207], [493, 219, 353, 351, 214, 492], [508, 227, 355, 356, 221, 506], [568, 564, 565, 563, 566, 567], [358, 229, 330, 332, 116, 357], [329, 206, 205, 207, 208, 328], [356, 221, 220, 218, 219, 353], [565, 508, 506, 507, 505, 564], [568, 501, 502, 229, 358, 567], [332, 328, 329, 327, 331, 330], [205, 621, 620, 29, 206], [494, 348, 215, 218, 219, 493], [557, 220, 221, 506, 507, 554], [568, 501, 551, 553, 505, 564], [503, 343, 331, 330, 229, 502], [329, 206, 29, 101, 102, 327], [559, 486, 215, 218, 220, 557], [556, 552, 553, 505, 507, 554], [551, 501, 502, 503, 504, 550], [344, 114, 102, 327, 331, 343], [101, 29, 623, 622, 99], [561, 347, 348, 215, 486, 560], [559, 557, 554, 556, 555, 558], [591, 550, 551, 553, 552, 588], [504, 346, 345, 344, 343, 503], [115, 100, 99, 101, 102, 114], [593, 558, 559, 486, 560, 592], [588, 552, 556, 555, 485, 587], [591, 550, 504, 346, 546, 590], [345, 339, 342, 115, 114, 344], [99, 625, 624, 37, 100], [607, 562, 561, 560, 592, 605], [594, 488, 485, 555, 558, 593], [591, 588, 587, 586, 589, 590], [548, 482, 339, 345, 346, 546], [342, 115, 100, 37, 40, 340], [611, 605, 592, 593, 594, 610], [587, 485, 488, 487, 484, 586], [590, 546, 548, 547, 549, 589], [482, 339, 342, 340, 341, 481], [37, 626, 627, 39, 40], [611, 605, 607, 606, 609], [610, 594, 488, 487, 608], [589, 549, 483, 484, 586], [548, 482, 481, 480, 547], [341, 38, 39, 40, 340], [609, 611, 610, 608, 628, 629], [608, 487, 484, 483, 631, 630], [483, 549, 547, 480, 633, 632], [480, 481, 341, 38, 635, 634], [38, 39, 636, 637], [537, 419, 385, 365, 363, 535], [539, 23, 22, 1, 128, 538], [146, 43, 44, 46, 45, 145], [42, 13, 12, 21, 20, 41], [18, 11, 10, 9, 8, 17], [539, 23, 231, 364, 363, 535], [282, 22, 1, 45, 145, 281], [147, 67, 20, 41, 43, 146], [64, 18, 11, 12, 21, 63], [638, 55, 17, 8, 639], [515, 510, 364, 363, 365, 514], [283, 230, 231, 23, 22, 282], [442, 147, 146, 145, 281, 438], [152, 63, 21, 20, 67, 149], [65, 59, 55, 17, 18, 64], [510, 364, 231, 230, 232, 509], [439, 284, 283, 282, 281, 438], [442, 147, 67, 149, 150, 440], [153, 66, 65, 64, 63, 152], [640, 57, 59, 55, 641], [572, 516, 515, 510, 509, 571], [284, 120, 122, 232, 230, 283], [442, 438, 439, 437, 441, 440], [153, 151, 148, 150, 149, 152], [66, 56, 58, 57, 59, 65], [571, 509, 232, 122, 123, 569], [439, 284, 120, 121, 62, 437], [441, 395, 392, 148, 150, 440], [153, 66, 56, 60, 61, 151], [643, 54, 58, 57, 642], [574, 570, 569, 571, 572, 573], [375, 123, 122, 120, 121, 372], [441, 395, 396, 19, 62, 437], [393, 144, 61, 151, 148, 392], [408, 54, 58, 56, 60, 404], [570, 124, 376, 375, 123, 569], [373, 0, 19, 62, 121, 372], [397, 394, 393, 392, 395, 396], [406, 256, 144, 61, 60, 404], [645, 407, 408, 54, 644], [574, 545, 293, 233, 124, 570], [377, 374, 373, 372, 375, 376], [397, 248, 5, 0, 19, 396], [394, 251, 255, 256, 144, 393], [409, 405, 406, 404, 408, 407], [377, 370, 367, 233, 124, 376], [374, 235, 84, 5, 0, 373], [397, 248, 249, 250, 251, 394], [532, 255, 256, 406, 405, 529], [646, 254, 409, 407, 647], [368, 234, 294, 293, 233, 367], [377, 370, 371, 236, 235, 374], [249, 127, 83, 84, 5, 248], [534, 476, 250, 251, 255, 532], [531, 402, 254, 409, 405, 529], [371, 369, 366, 368, 367, 370], [236, 81, 82, 83, 84, 235], [478, 323, 127, 249, 250, 476], [534, 532, 529, 531, 530, 533], [648, 400, 402, 254, 649], [368, 234, 167, 69, 28, 366], [371, 236, 81, 87, 86, 369], [325, 203, 82, 83, 127, 323], [534, 476, 478, 477, 479, 533], [531, 402, 400, 401, 403, 530], [369, 86, 93, 90, 28, 366], [204, 89, 87, 81, 82, 203], [478, 323, 325, 324, 326, 477], [533, 479, 399, 398, 403, 530], [650, 243, 401, 400, 651], [98, 70, 69, 28, 90, 96], [93, 86, 87, 89, 88, 92], [325, 203, 204, 322, 318, 324], [479, 399, 252, 253, 326, 477], [403, 398, 242, 244, 243, 401], [96, 90, 93, 92, 91, 95], [322, 204, 89, 88, 85, 321], [326, 253, 245, 319, 318, 324], [399, 252, 246, 126, 242, 398], [653, 241, 244, 243, 652], [98, 96, 95, 94, 97], [92, 88, 85, 27, 91], [322, 318, 319, 320, 321], [253, 245, 247, 246, 252], [244, 241, 125, 126, 242], [655, 654, 94, 95, 91, 27], [657, 656, 27, 85, 321, 320], [658, 659, 320, 319, 245, 247], [661, 660, 247, 246, 126, 125], [662, 125, 241, 663], [537, 419, 385, 365, 363, 535], [384, 238, 239, 379, 378, 383], [527, 391, 240, 521, 518, 526], [525, 386, 104, 34, 118, 524], [110, 105, 106, 107, 109, 108], [514, 365, 385, 383, 378, 512], [521, 240, 239, 379, 380, 520], [526, 518, 519, 387, 386, 525], [338, 107, 106, 34, 104, 333], [109, 24, 664, 665, 108], [515, 510, 364, 363, 365, 514], [513, 381, 380, 379, 378, 512], [522, 517, 519, 518, 521, 520], [387, 211, 335, 333, 104, 386], [338, 107, 109, 24, 4, 337], [516, 511, 513, 512, 514, 515], [522, 473, 470, 381, 380, 520], [519, 387, 211, 210, 177, 517], [338, 333, 335, 334, 336, 337], [3, 667, 666, 24, 4], [572, 516, 515, 510, 509, 571], [513, 381, 470, 471, 295, 511], [522, 473, 475, 460, 177, 517], [335, 211, 210, 209, 212, 334], [337, 4, 3, 301, 305, 336], [573, 542, 295, 511, 516, 572], [475, 473, 470, 471, 472, 474], [461, 306, 209, 210, 177, 460], [336, 305, 304, 175, 212, 334], [300, 669, 668, 3, 301], [574, 570, 569, 571, 572, 573], [544, 457, 472, 471, 295, 542], [475, 460, 461, 462, 463, 474], [307, 176, 175, 212, 209, 306], [305, 301, 300, 302, 303, 304], [574, 545, 543, 544, 542, 573], [474, 463, 455, 458, 457, 472], [467, 307, 306, 461, 462, 465], [304, 175, 176, 299, 297, 303], [173, 670, 671, 300, 302], [574, 545, 293, 233, 124, 570], [544, 457, 458, 459, 456, 543], [465, 462, 463, 455, 454, 464], [468, 310, 299, 176, 307, 467], [303, 297, 298, 174, 173, 302], [545, 293, 294, 292, 456, 543], [459, 452, 453, 454, 455, 458], [469, 466, 464, 465, 467, 468], [311, 296, 298, 297, 299, 310], [2, 672, 673, 173, 174], [368, 234, 294, 293, 233, 367], [459, 452, 194, 166, 292, 456], [466, 195, 196, 453, 454, 464], [469, 308, 309, 311, 310, 468], [298, 174, 2, 198, 200, 296], [294, 234, 167, 165, 166, 292], [453, 196, 317, 314, 194, 452], [469, 308, 178, 183, 195, 466], [311, 296, 200, 201, 73, 309], [197, 675, 674, 2, 198], [368, 234, 167, 69, 28, 366], [314, 194, 166, 165, 72, 313], [317, 196, 195, 183, 181, 315], [309, 73, 75, 180, 178, 308], [202, 199, 197, 198, 200, 201], [167, 69, 70, 71, 72, 165], [317, 314, 313, 312, 316, 315], [183, 178, 180, 179, 182, 181], [202, 79, 74, 75, 73, 201], [77, 676, 677, 197, 199], [98, 70, 69, 28, 90, 96], [313, 72, 71, 170, 172, 312], [316, 185, 187, 182, 181, 315], [193, 74, 75, 180, 179, 189], [202, 79, 80, 78, 77, 199], [170, 71, 70, 98, 97, 169], [316, 185, 186, 171, 172, 312], [190, 188, 187, 182, 179, 189], [193, 74, 79, 80, 26, 192], [78, 76, 679, 678, 77], [98, 96, 95, 94, 97], [172, 170, 169, 168, 171], [188, 184, 186, 185, 187], [193, 189, 190, 191, 192], [80, 26, 25, 76, 78], [680, 681, 168, 169, 97, 94], [682, 683, 184, 186, 171, 168], [684, 685, 191, 190, 188, 184], [687, 686, 25, 26, 192, 191], [689, 688, 76, 25], [537, 419, 385, 365, 363, 535], [539, 23, 22, 1, 128, 538], [146, 43, 44, 46, 45, 145], [42, 13, 12, 21, 20, 41], [18, 11, 10, 9, 8, 17], [540, 536, 537, 535, 539, 538], [129, 47, 46, 45, 1, 128], [429, 44, 43, 41, 42, 427], [140, 10, 11, 12, 13, 137], [691, 8, 9, 6, 690], [537, 419, 418, 417, 416, 536], [540, 262, 260, 129, 128, 538], [430, 134, 47, 46, 44, 429], [427, 42, 13, 137, 139, 426], [142, 50, 6, 9, 10, 140], [540, 262, 421, 425, 416, 536], [260, 129, 47, 134, 136, 259], [431, 428, 426, 427, 429, 430], [142, 140, 137, 139, 138, 141], [693, 6, 50, 49, 692], [425, 416, 417, 162, 213, 423], [422, 261, 259, 260, 262, 421], [431, 264, 135, 136, 134, 430], [428, 265, 52, 138, 139, 426], [142, 50, 49, 51, 48, 141], [425, 421, 422, 420, 424, 423], [261, 133, 132, 135, 136, 259], [431, 264, 263, 266, 265, 428], [141, 48, 15, 14, 52, 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      "--\n",
      "[[-1.05107606 -1.3962634 ]\n",
      " [-0.83387953  0.        ]\n",
      " [ 2.71883512 -1.74532925]\n",
      " ...\n",
      " [-2.51327412  9.09665606]\n",
      " [-8.65295458  2.7925268 ]\n",
      " [-2.51327412  9.09665606]]\n",
      "Vertices:  [[-1.05107606 -1.3962634 ]\n",
      " [-0.83387953  0.        ]\n",
      " [ 2.71883512 -1.74532925]\n",
      " ...\n",
      " [ 0.          3.1625366 ]\n",
      " [ 0.42275753  2.7925268 ]\n",
      " [ 0.205561    2.7925268 ]]\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.spatial import Voronoi\n",
    "\n",
    "def voronoi_finite_polygons_2d(vor, radius=None):\n",
    "    \"\"\"\n",
    "    Reconstruct infinite voronoi regions in a 2D diagram to finite\n",
    "    regions.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    vor : Voronoi\n",
    "        Input diagram\n",
    "    radius : float, optional\n",
    "        Distance to 'points at infinity'.\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    regions : list of tuples\n",
    "        Indices of vertices in each revised Voronoi regions.\n",
    "    vertices : list of tuples\n",
    "        Coordinates for revised Voronoi vertices. Same as coordinates\n",
    "        of input vertices, with 'points at infinity' appended to the\n",
    "        end.\n",
    "\n",
    "    \"\"\"\n",
    "\n",
    "    if vor.points.shape[1] != 2:\n",
    "        raise ValueError(\"Requires 2D input\")\n",
    "\n",
    "    new_regions = []\n",
    "    new_vertices = vor.vertices.tolist()\n",
    "\n",
    "    center = vor.points.mean(axis=0)\n",
    "    if radius is None:\n",
    "        radius = vor.points.ptp().max()\n",
    "\n",
    "    # Construct a map containing all ridges for a given point\n",
    "    all_ridges = {}\n",
    "    for (p1, p2), (v1, v2) in zip(vor.ridge_points, vor.ridge_vertices):\n",
    "        all_ridges.setdefault(p1, []).append((p2, v1, v2))\n",
    "        all_ridges.setdefault(p2, []).append((p1, v1, v2))\n",
    "\n",
    "    # Reconstruct infinite regions\n",
    "    for p1, region in enumerate(vor.point_region):\n",
    "        vertices = vor.regions[region]\n",
    "\n",
    "        if all(v >= 0 for v in vertices):\n",
    "            # finite region\n",
    "            new_regions.append(vertices)\n",
    "            continue\n",
    "\n",
    "        # reconstruct a non-finite region\n",
    "        ridges = all_ridges[p1]\n",
    "        new_region = [v for v in vertices if v >= 0]\n",
    "\n",
    "        for p2, v1, v2 in ridges:\n",
    "            if v2 < 0:\n",
    "                v1, v2 = v2, v1\n",
    "            if v1 >= 0:\n",
    "                # finite ridge: already in the region\n",
    "                continue\n",
    "\n",
    "            # Compute the missing endpoint of an infinite ridge\n",
    "\n",
    "            t = vor.points[p2] - vor.points[p1] # tangent\n",
    "            t /= np.linalg.norm(t)\n",
    "            n = np.array([-t[1], t[0]])  # normal\n",
    "\n",
    "            midpoint = vor.points[[p1, p2]].mean(axis=0)\n",
    "            direction = np.sign(np.dot(midpoint - center, n)) * n\n",
    "            far_point = vor.vertices[v2] + direction * radius\n",
    "\n",
    "            new_region.append(len(new_vertices))\n",
    "            new_vertices.append(far_point.tolist())\n",
    "\n",
    "        # sort region counterclockwise\n",
    "        vs = np.asarray([new_vertices[v] for v in new_region])\n",
    "        c = vs.mean(axis=0)\n",
    "        angles = np.arctan2(vs[:,1] - c[1], vs[:,0] - c[0])\n",
    "        new_region = np.array(new_region)[np.argsort(angles)]\n",
    "\n",
    "        # finish\n",
    "        new_regions.append(new_region.tolist())\n",
    "\n",
    "    return new_regions, np.asarray(new_vertices)\n",
    "\n",
    "# make up data points\n",
    "np.random.seed(1234)\n",
    "points = earth_array\n",
    "\n",
    "# compute Voronoi tesselation\n",
    "vor = Voronoi(points)\n",
    "\n",
    "# plot\n",
    "regions, vertices = voronoi_finite_polygons_2d(vor)\n",
    "print (\"--\")\n",
    "print (regions)\n",
    "print (\"--\")\n",
    "print (vertices)\n",
    "print (\"Vertices: \",vor.vertices)\n",
    "#import pdb\n",
    "#pdb.set_trace()\n",
    "\n",
    "# colorize\n",
    "for region in regions:\n",
    "    polygon = vertices[region]\n",
    "    plt.fill(*zip(*polygon), alpha=0.4)\n",
    "\n",
    "plt.plot(points[:,0], points[:,1], 'ko')\n",
    "plt.xlim(vor.min_bound[0] - 0.1, vor.max_bound[0] + 0.1)\n",
    "plt.ylim(vor.min_bound[1] - 0.1, vor.max_bound[1] + 0.1)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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[[-1.7763573275853397, 2.2689280275926285], [-1.9935538567224118, 2.2689280275926285]], [[-1.9935538567224118, 2.2689280275926285], [-2.090516592944319, 2.4434609527920617]], [[-2.090516592944319, 2.4434609527920617], [-1.9935538567224118, 2.6179938779914944]], [[-1.9935538567224118, 2.6179938779914944], [-1.7763573275853397, 2.6179938779914944]], [[-1.7763573275853397, 2.6179938779914944], [-1.6793945913634327, 2.4434609527920617]], [[-2.3077131220813913, 2.4434609527920617], [-2.4046758583032983, 2.2689280275926285]], [[-2.4046758583032983, 2.2689280275926285], [-2.6218723874403707, 2.268928027592628]], [[-2.6218723874403707, 2.268928027592628], [-2.7188351236622776, 2.443460952792061]], [[-2.7188351236622776, 2.443460952792061], [-2.6218723874403707, 2.617993877991494]], [[-2.6218723874403707, 2.617993877991494], [-2.4046758583032983, 2.617993877991494]], [[-2.4046758583032983, 2.617993877991494], [-2.3077131220813913, 2.4434609527920617]], [[-0.20556100079044315, 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2.4434609527920617]], [[-1.4621980622263604, 2.4434609527920617], [-1.6793945913634327, 2.4434609527920617]], [[-1.6793945913634327, 2.4434609527920617], [-1.7763573275853397, 2.6179938779914944]], [[-1.7763573275853397, 2.6179938779914944], [-1.6793945913634327, 2.792526803190927]], [[-1.6793945913634327, 2.792526803190927], [-1.4621980622263604, 2.792526803190927]], [[-1.4621980622263604, 2.792526803190927], [-1.3652353260044534, 2.6179938779914944]], [[-1.3652353260044534, 2.6179938779914944], [-1.4621980622263604, 2.4434609527920617]], [[-2.090516592944319, 2.4434609527920617], [-2.3077131220813913, 2.4434609527920617]], [[-2.3077131220813913, 2.4434609527920617], [-2.4046758583032983, 2.617993877991494]], [[-2.4046758583032983, 2.617993877991494], [-2.3077131220813913, 2.792526803190927]], [[-2.3077131220813913, 2.792526803190927], [-2.090516592944319, 2.792526803190927]], [[-2.090516592944319, 2.792526803190927], [-1.9935538567224118, 2.6179938779914944]], [[-1.9935538567224118, 2.6179938779914944], [-2.090516592944319, 2.4434609527920617]], [[-2.7188351236622776, 2.443460952792061], [-2.6218723874403707, 2.617993877991494]], [[-2.6218723874403707, 2.617993877991494], [-2.7188351236622776, 2.792526803190927]], [[0.20556100079044315, 2.792526803190927], [0.10859826456853607, 2.617993877991494]], [[0.10859826456853607, 2.617993877991494], [-0.10859826456853607, 2.617993877991494]], [[-0.10859826456853607, 2.617993877991494], [-0.20556100079044315, 2.792526803190927]], [[-0.20556100079044315, 2.792526803190927], [0.0, 3.162536604613725]], [[-0.7369167952864947, 2.6179938779914944], [-0.5197202661494226, 2.6179938779914944]], [[-0.5197202661494226, 2.6179938779914944], [-0.4227575299275155, 2.792526803190927]], [[-0.4227575299275155, 2.792526803190927], [-0.6283185307179586, 3.162536604613725]], [[-0.8338795315084018, 2.792526803190927], [-0.7369167952864947, 2.6179938779914944]], [[-1.4621980622263604, 2.792526803190927], [-1.3652353260044534, 2.6179938779914944]], [[-1.3652353260044534, 2.6179938779914944], [-1.1480387968673813, 2.6179938779914944]], [[-1.1480387968673813, 2.6179938779914944], [-1.051076060645474, 2.792526803190927]], [[-1.051076060645474, 2.792526803190927], [-1.2566370614359172, 3.162536604613725]], [[-1.6793945913634327, 2.792526803190927], [-1.7763573275853397, 2.6179938779914944]], [[-1.7763573275853397, 2.6179938779914944], [-1.9935538567224118, 2.6179938779914944]], [[-1.9935538567224118, 2.6179938779914944], [-2.090516592944319, 2.792526803190927]], [[-2.090516592944319, 2.792526803190927], [-1.8849555921538759, 3.162536604613725]], [[-2.4046758583032983, 2.617993877991494], [-2.3077131220813913, 2.792526803190927]], [[-2.3077131220813913, 2.792526803190927], [-2.5132741228718345, 3.1625366046137255]], [[-2.7188351236622776, 2.792526803190927], [-2.6218723874403707, 2.617993877991494]], [[-2.6218723874403707, 2.617993877991494], [-2.4046758583032983, 2.617993877991494]], [[-0.4227575299275155, 2.792526803190927], [-0.20556100079044315, 2.792526803190927]], [[-0.20556100079044315, 2.792526803190927], [0.0, 3.162536604613725]], [[-1.051076060645474, 2.792526803190927], [-0.8338795315084018, 2.792526803190927]], [[-0.8338795315084018, 2.792526803190927], [-0.6283185307179586, 3.162536604613725]], [[-1.6793945913634327, 2.792526803190927], [-1.4621980622263604, 2.792526803190927]], [[-1.4621980622263604, 2.792526803190927], [-1.2566370614359172, 3.162536604613725]], [[-2.3077131220813913, 2.792526803190927], [-2.090516592944319, 2.792526803190927]], [[-2.090516592944319, 2.792526803190927], [-1.8849555921538759, 3.162536604613725]], [[-2.7188351236622776, 2.792526803190927], [-2.5132741228718345, 3.1625366046137255]]]\n"
     ]
    }
   ],
   "source": [
    "#compute edges based on the above\n",
    "edges = []\n",
    "for region in regions:\n",
    "    prev = region[-1]\n",
    "    for now in region:\n",
    "        if (vertices[prev][0]< math.pi) and (vertices[prev][1]< math.pi) and (vertices[now][0]< math.pi) and (vertices[prev][1]< math.pi):\n",
    "            if (vertices[prev][0]> -math.pi) and (vertices[prev][1]> -math.pi) and (vertices[now][0]>- math.pi) and (vertices[prev][1]>- math.pi):\n",
    "                edges.append([vertices[prev].tolist(), vertices[now].tolist()])\n",
    "        prev = now\n",
    "print(edges)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "edges2 = []\n",
    "for vertex in vor.ridge_vertices:\n",
    "    if vertex != -1:\n",
    "        vor.vertices\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.0000000e+00 1.2246468e-16]\n",
      " [1.2246468e-16 0.0000000e+00]]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics.pairwise import haversine_distances\n",
    "from math import radians\n",
    "test_1= [math.pi/2, math.pi]\n",
    "test_2= [math.pi/2, 0]\n",
    "print(haversine_distances( [test_1, test_2]))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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