#include <math.h>

#include "geography.h"
#include "more_math.h"

// changed constants to preprocessor variables (b/c initializers of global
// constants can't refer to other variables, whether they're constant or not)
#define NORTH_POLE_LATITUDE (PI / 2)
#define EARTH_RADIUS_MILES 3959.0

/**
 * Computes the distance of the great circle route between two points.
 * The latitudes and longitudes should be in degrees and the distance
 * is computes assuming that the Earth is spherical.
 *
 * @param lat1 a double between -90 and +90
 * @param lon1 a double between -180 and 180
 * @param lat2 a double between -90 and +90
 * @param lon2 a double between -180 and 180
 * @return the distance between (lat1, lon1) and (lat2, lon2)
 */
double distance(const location *from, const location *to)
{
  // convert latitudes to radians and get colatitude
  double colat1 = colatitude(to_radians(from->lat));
  double colat2 = colatitude(to_radians(to->lat));

  // compute difference in longitudes in radians
  double delta_lon = to_radians(from->lon - to->lon);

  // use spherical law of cosines to compute angle
  double x = acos(cos(colat1) * cos(colat2) + sin(colat1) * sin(colat2) * cos(delta_lon));

  // convert radians to arc length by multiplying by radius
  return x * EARTH_RADIUS_MILES;
}

/**
 * Returns the colatitude of the given latitude in degrees.  The given latitude
 * should be in degrees.
 *
 * @param lat a double between -90 and +90
 * @return the colatitude of lat, in degrees
 */
double colatitude(double lat)
{
  return NORTH_POLE_LATITUDE - lat;
}