#include <math.h>
#include <stdio.h>

/**
 * Calculate and output the distance between two points given their
 * latitudes and longitues in degrees.  We assume the Earth is a
 * sphere with radius 3959 miles.
 * 
 * Compile and link with
 * gcc -c -Wall -std=c99 -pedantic distance.c
 * gcc -o Distance distance.o -lm
 *
 * -Wall turns on all compiler warnings, most of them helpful
 * -std=c99 tells the compiler to use the 1999 version of C (languages evolve)
 * -pedantic tells the compiler not to use gcc-specific extensions to C99
 * 
 * -lm tells the linker to link the math library into the executable;
 * that is the only C library that requires such special treatment
 *
 * From the command line on the Zoo, you can copy this into your current
 * working directory with
 *
 * cp /c/cs223/www/Examples/distance.c .
 *
 * @version 0.1 2018-09-04
 */

// declare some global constants for readability
const double PI = 3.14159265358979;
const double EARTH_RADIUS_MILES = 3959;

// *declare* my functions (names and argument/return types - no body)

// I also write Javadoc-style comments here (there are tools to
// convert these comments into reference material)
/**
 * Converts the given angle to degrees.
 *
 * @param deg a non-infinite double-precision floating point number
 * @return the value of that angle in radians
 */
double to_radians(double deg);

/**
 * Converts the given latitude to colatitude.  Latitude measures from
 * the equator; colatitude measures from the north pole.
 *
 * @param deg a double between -90 and 90
 * @return the corresponding colatitude
 */
double colatitude(double deg);

int main()
{
  double lat1; // double/float: numeric values w/ fractional part
  // int/short/long: integers (numbers w/ no fractional part)
  // gcc on Zoo allows ints to be +/- 2billion
  // char: a single character (letter, digit, punctuation)
  double lon1;
  double lat2, lon2;

  // hard-code the coordinates for now (handle user input next time)
  // Tweed New Haven Airport (HVN)
  lat1 = 41.263750;
  lon1 = -72.886805;

  // London City Airport (LCY)
  lat2 = 51.505278;
  lon2 = 0.0552780;
  
  // convert degrees to radians
  lat1 = to_radians(lat1);
  lon1 = to_radians(lon1);
  lat2 = to_radians(lat2);
  lon2 = to_radians(lon2);

  // convert anglular distance from equator to angular distance from North Pole
  double colat1 = colatitude(lat1);
  double colat2 = colatitude(lat2);

  // calculate difference in longitudes
  double delta_lon = lon1 - lon2;
  
  // fun trig to compute angle subtended by great circle between two points
  // given their colatitudes and difference in longitudes
  double x = acos(cos(colat1) * cos(colat2) + sin(colat1) * sin(colat2) * cos(delta_lon));
  double dist = x * EARTH_RADIUS_MILES;
  
  // this will be off from true distance b/c we're assuming a spherical Earth
  printf("%f\n", dist); // %d for int; %f for float
  
  return 0;
}
  
double to_radians(double deg)
{
  return deg / 180 * PI;
}

double colatitude(double deg)
{
  return PI / 2 - deg;
}