/// <summary>
/// lat= lat1+d*cos(tc)
/// IF (abs(lat) > pi/2) "d too large. You can't go this far along this rhumb line!"
/// IF (abs(lat-lat1) <![CDATA[<]]> sqrt(TOL)){
/// q=cos(lat1)
/// } ELSE {
/// dphi=log(tan(lat/2+pi/4)/tan(lat1/2+pi/4))
/// q= (lat-lat1)/dphi
/// }
/// dlon=-d*sin(tc)/q
/// lon=mod(lon1+dlon+pi,2*pi)-pi
/// </summary>
/// <param name="coordinate"></param>
/// <returns></returns>
public Coordinate Rhumb(Coordinate coordinate)
{
var latitude = new Latitude(coordinate.Latitude + Bearing.Cos() * Distance);
if (latitude.Abs() > Angle.Pi / 2)
{
throw new ApplicationException("Distance too large. You can't go this far along this rhumb line!");
}
double q;
if ((latitude - coordinate.Latitude).Abs().Radians < 1E-15)
{
q = coordinate.Latitude.Cos();
}
else
{
var dphi = Angle.FromRadians(Math.Log((latitude / 2 + Angle.Pi / 4).Tan() / (coordinate.Latitude / 2 + Angle.Pi / 4).Tan()));
q = (latitude - coordinate.Latitude) / dphi;
}
var dlon = -Distance *Bearing.Sin() / q;
var longitude = new Longitude((coordinate.Longitude + dlon + Angle.Pi) % (2 * Angle.Pi) - Angle.Pi);
return(new Coordinate(latitude, longitude));
}
