Show the calculated distance in meters between three points with the same longitude using different coordinate systems/methods.

Compare distance calculations in different coordinate systems.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "3de7bed1",
   "metadata": {},
   "outputs": [],
   "source": [
    "import shapely.geometry\n",
    "import fiona.transform\n",
    "import geopy.distance\n",
    "\n",
    "seattle_lon, seattle_lat = -122, 47\n",
    "san_fransisco_lon, san_fransisco_lat = -122, 38\n",
    "some_other_lon, some_other_lat = -122, 56"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "cdfbc4ca",
   "metadata": {},
   "outputs": [],
   "source": [
    "seattle_geom = shapely.geometry.mapping(shapely.geometry.Point(seattle_lon, seattle_lat))\n",
    "san_fransisco_geom = shapely.geometry.mapping(shapely.geometry.Point(san_fransisco_lon, san_fransisco_lat))\n",
    "some_other_geom = shapely.geometry.mapping(shapely.geometry.Point(some_other_lon, some_other_lat))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "74344d0f",
   "metadata": {},
   "outputs": [],
   "source": [
    "seattle_utm = shapely.geometry.shape(fiona.transform.transform_geom(\"epsg:4326\", \"EPSG:32610\", seattle_geom))\n",
    "san_fransisco_utm = shapely.geometry.shape(fiona.transform.transform_geom(\"epsg:4326\", \"EPSG:32610\", san_fransisco_geom))\n",
    "some_other_utm = shapely.geometry.shape(fiona.transform.transform_geom(\"epsg:4326\", \"EPSG:32610\", some_other_geom))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "06cfe70e",
   "metadata": {},
   "outputs": [],
   "source": [
    "seattle_equal_area = shapely.geometry.shape(fiona.transform.transform_geom(\"epsg:4326\", \"EPSG:6933\", seattle_geom))\n",
    "san_fransisco_equal_area = shapely.geometry.shape(fiona.transform.transform_geom(\"epsg:4326\", \"EPSG:6933\", san_fransisco_geom))\n",
    "some_other_equal_area = shapely.geometry.shape(fiona.transform.transform_geom(\"epsg:4326\", \"EPSG:6933\", some_other_geom))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "c7751a80",
   "metadata": {},
   "outputs": [],
   "source": [
    "seattle_bad = shapely.geometry.shape(fiona.transform.transform_geom(\"epsg:4326\", \"EPSG:3857\", seattle_geom))\n",
    "san_fransisco_bad = shapely.geometry.shape(fiona.transform.transform_geom(\"epsg:4326\", \"EPSG:3857\", san_fransisco_geom))\n",
    "some_other_bad = shapely.geometry.shape(fiona.transform.transform_geom(\"epsg:4326\", \"EPSG:3857\", some_other_geom))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "503b0646",
   "metadata": {},
   "outputs": [],
   "source": [
    "seattle_azimuthal = shapely.geometry.shape(fiona.transform.transform_geom(\"epsg:4326\", \"ESRI:102016\", seattle_geom))\n",
    "san_fransisco_azimuthal = shapely.geometry.shape(fiona.transform.transform_geom(\"epsg:4326\", \"ESRI:102016\", san_fransisco_geom))\n",
    "some_other_azimuthal = shapely.geometry.shape(fiona.transform.transform_geom(\"epsg:4326\", \"ESRI:102016\", some_other_geom))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "625b5f1a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(999431.9345002294, 1000974.6564423705)"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#%%timeit -n 10000 -r 7\n",
    "seattle_utm.distance(san_fransisco_utm), seattle_utm.distance(some_other_utm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "3e2ea858",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(850814.3446692536, 719874.2665405516)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#%%timeit -n 10000 -r 7\n",
    "seattle_equal_area.distance(san_fransisco_equal_area), seattle_equal_area.distance(some_other_equal_area)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "23c38992",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1362648.2595610106, 1616341.5836506737)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#%%timeit -n 10000 -r 7\n",
    "seattle_bad.distance(san_fransisco_bad), seattle_bad.distance(some_other_bad)  # technically meters but shouldn't be used for distances at all!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "969e8ad0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(999748.9898021035, 1001316.0035028645)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#%%timeit -n 10000 -r 7\n",
    "seattle_azimuthal.distance(san_fransisco_azimuthal), seattle_azimuthal.distance(some_other_azimuthal)  # https://epsg.io/102016"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "21e31fd5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(999748.9898013712, 1001316.003501355)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#%%timeit\n",
    "geopy.distance.distance((seattle_lat, seattle_lon), (san_fransisco_lat, san_fransisco_lon)).m, geopy.distance.distance((seattle_lat, seattle_lon), (some_other_lat, some_other_lon)).m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "c8f5561d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1000755.7535177224, 1000755.7535177228)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#%%timeit\n",
    "geopy.distance.great_circle((seattle_lat, seattle_lon), (san_fransisco_lat, san_fransisco_lon)).m, geopy.distance.great_circle((seattle_lat, seattle_lon), (some_other_lat, some_other_lon)).m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4baa0887",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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