{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example usage\n",
    "\n",
    "To use `karney` in a project:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0.2\n"
     ]
    }
   ],
   "source": [
    "import karney\n",
    "\n",
    "print(karney.__version__)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Surface distance\n",
    "    \n",
    "Find the surface distance sAB (i.e. great circle distance) between two\n",
    "positions A and B. The heights of A and B are ignored, i.e. if they don't have\n",
    "zero height, we seek the distance between the points that are at the surface of\n",
    "the Earth, directly above/below A and B.  Use Earth radius 6371e3 m.\n",
    "Compare the results with exact calculations for the WGS-84 ellipsoid.\n",
    "\n",
    "In geodesy this is known as \"The second geodetic problem\" or\n",
    "\"The inverse geodetic problem\" for a sphere/ellipsoid.\n",
    "\n",
    "### Solution for a sphere:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Ex5: Great circle = 332.46 km'"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from karney.geodesic import rad, sphere_distance_rad, distance\n",
    "\n",
    "latlon_a = (88, 0)\n",
    "latlon_b = (89, -170)\n",
    "latlons = latlon_a + latlon_b\n",
    "r_Earth = 6371e3  # m, mean Earth radius\n",
    "s_AB = sphere_distance_rad(*rad(latlons))[0]*r_Earth\n",
    "s_AB = distance(*latlons, a=r_Earth, f=0, degrees=True)[0] # or alternatively\n",
    "\n",
    "\"Ex5: Great circle = {:5.2f} km\".format(s_AB / 1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exact solution for the WGS84 ellipsoid:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Ellipsoidal distance = 333.95 km'"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s_12, azi1, azi2 = distance(*latlons, degrees=True)\n",
    "\"Ellipsoidal distance = {:5.2f} km\".format(s_12 / 1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A and azimuth/distance to B\n",
    "    \n",
    "We have an initial position A, direction of travel given as an azimuth\n",
    "(bearing) relative to north (clockwise), and finally the\n",
    "distance to travel along a great circle given as sAB.\n",
    "Use Earth radius 6371e3 m to find the destination point B.\n",
    "\n",
    "In geodesy this is known as \"The first geodetic problem\" or\n",
    "\"The direct geodetic problem\" for a sphere.\n",
    "\n",
    "    \n",
    "### Greatcircle solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Ex8, Destination: lat, lon = 79.9915 deg, -90.0177 deg'"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from karney.geodesic import reckon\n",
    "lat, lon = 80, -90\n",
    "\n",
    "lat2, lon2, azi_b = reckon(lat, lon, distance=1000, azimuth=200, a=6371e3, f=0, degrees=True)\n",
    "\n",
    "msg = \"Ex8, Destination: lat, lon = {:4.4f} deg, {:4.4f} deg\"\n",
    "msg.format(lat2, lon2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(azi_b, -160.0174292682187)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exact solution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Ex8, Destination: lat, lon = 79.9916 deg, -90.0176 deg'"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lat_b, lon_b, azi_b = reckon(lat, lon, distance=1000, azimuth=200, degrees=True)\n",
    "msg.format(lat_b, lon_b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(azi_b, -160.01742926820506)"
   ]
  }
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