/// <summary>
/// Initial course of great circle going to coordinate
///
/// From http://williams.best.vwh.net/avform.htm:
///
/// mod
/// ( atan2
/// ( sin(lon1-lon2) * cos(lat2)
/// , cos(lat1)*sin(lat2) - sin(lat1)*cos(lat2)*cos(lon1-lon2)
/// )
/// , 2*pi
/// )
/// </summary>
/// <param name="coordinate">Target coordinate that we want to travel to</param>
/// <returns>initial bearing</returns>
public Bearing InitialCourse(Coordinate coordinate)
{
// TODO: resolve edge case: close to the poles
// if (Latitude.Cos() < .0001)
// return Latitude.Hemisphere == Latitude.HemisphereType.North ? Bearing.South : Bearing.North;
return(new Bearing(Angle.Atan2((Longitude - coordinate.Longitude).Sin() * coordinate.Latitude.Cos(), Latitude.Cos() * coordinate.Latitude.Sin() -
Latitude.Sin() * coordinate.Latitude.Cos() * (Longitude - coordinate.Longitude).Cos())));
}
/// <summary>
/// lat =asin(sin(lat1)*cos(d)+cos(lat1)*sin(d)*cos(tc))
/// dlon=atan2(sin(tc)*sin(d)*cos(lat1),cos(d)-sin(lat1)*sin(lat))
/// lon=mod( lon1-dlon +pi,2*pi )-pi
/// </summary>
/// <param name="coordinate"></param>
/// <returns></returns>
public Coordinate GreatCircle(Coordinate coordinate)
{
var latitude = new Latitude(
Angle.Asin(coordinate.Latitude.Sin() * Distance.Cos() + coordinate.Latitude.Cos() * Distance.Sin() * Bearing.Cos()));
var dlon = Angle.Atan2(Bearing.Sin() * Distance.Sin() * coordinate.Latitude.Cos(),
Distance.Cos() - coordinate.Latitude.Sin() * latitude.Sin());
var longitude = new Longitude((coordinate.Longitude - dlon + Angle.Pi) % (2 * Angle.Pi) - Angle.Pi);
return(new Coordinate(latitude, longitude));
}
public Angle Atan2()
{
return(Angle.Atan2(X, Y));
}