/// <summary>
/// Get <see cref="CoordinatePoint" /> at distance and direction on an ellipsoid.
/// </summary>
/// <param name="basePoint">Source <see cref="CoordinatePoint"/>.</param>
/// <param name="distance">Distance to a new point, meters.</param>
/// <param name="azimuth">Azimuth to a new point, radians.</param>
/// <param name="backAzimuth">Azimuth from a new point to base point, radians.</param>
/// <returns><see cref="CoordinatePoint" /> at specified distance and direction from the base point.</returns>
public static CoordinatePoint GetCoordinatePointAtDistanceAndDirectionOnAnEllipsoid(CoordinatePoint basePoint, LinearDimension distance, double azimuth, out double backAzimuth)
{
double deltaLatitude;
double deltaLongitude;
double deltaAzimuth;
double newDeltaLatitude = 0;
double newDeltaLongitude = 0;
double newDeltaAzimuth = 0;
do
{
deltaLatitude = newDeltaLatitude;
deltaLongitude = newDeltaLongitude;
deltaAzimuth = newDeltaAzimuth;
double iterationLatitude = basePoint.Latitude.ToRadians() + deltaLatitude / 2;
double iterationAzimuth = azimuth + deltaAzimuth / 2;
double beta = distance.GetMeters() * Math.Cos(iterationAzimuth) / GetMeridionalForLatitude(Latitude.FromRadians(iterationLatitude));
double sigma = distance.GetMeters() * Math.Sin(iterationAzimuth) / (GetPrimeVerticalForLatitude(Latitude.FromRadians(iterationLatitude)) * Math.Cos(iterationLatitude));
double alpha = deltaLongitude * Math.Sin(iterationLatitude);
newDeltaLatitude = beta * (1 + (2 * Math.Pow(sigma, 2d) + Math.Pow(alpha, 2d)) / 24);
newDeltaLongitude = sigma * (1 + (Math.Pow(alpha, 2d) - Math.Pow(beta, 2d)) / 24);
newDeltaAzimuth = alpha * (1 + (3 * Math.Pow(beta, 2d) + 2 * Math.Pow(sigma, 2d) - 2 * Math.Pow(alpha, 2d)) / 24);
}while (Math.Abs(newDeltaLatitude - deltaLatitude) > 0.0000001d || Math.Abs(deltaLongitude - newDeltaLongitude) > 0.0000001d);
backAzimuth = azimuth + newDeltaAzimuth + Math.PI;
return(new CoordinatePoint(Latitude.FromRadians(basePoint.Latitude.ToRadians() + newDeltaLatitude),
Longitude.FromRadians(basePoint.Longitude.ToRadians() + newDeltaLongitude)));
}
/// <summary>
/// Get <see cref="CoordinatePoint" /> at distance and direction on the flat.
/// </summary>
/// <param name="basePoint">Source <see cref="CoordinatePoint"/></param>
/// <param name="distance">Distance to a new point.</param>
/// <param name="azimuth">Direction from one point to another in radians.</param>
/// <returns><see cref="CoordinatePoint"/> at specified distance and direction from the given point.</returns>
public static CoordinatePoint GetCoordinatePointAtDistanceAndDirectionOnTheFlat(CoordinatePoint basePoint, LinearDimension distance, double azimuth)
{
var deltaLatitudeGrad = distance.GetMeters() * Math.Cos(azimuth) / (_earthWgs84MeanRadius * _d2R);
var deltaLongitudeGrad = distance.GetMeters() * Math.Sin(azimuth) / (_earthWgs84MeanRadius * _d2R);
return(new CoordinatePoint(basePoint.Latitude.ToDegrees() + deltaLatitudeGrad, basePoint.Longitude.ToDegrees() + deltaLongitudeGrad));
}
/// <summary>
/// Get <see cref="CoordinatePoint" /> at distance and direction on sphere with Haversine.
/// </summary>
/// <param name="basePoint">Source <see cref="CoordinatePoint"/>.</param>
/// <param name="distance">Distance to a new point, meters.</param>
/// <param name="azimuth">Azimuth to a new point, radians.</param>
/// <param name="backAzimuth">Azimuth from a new point to base point, radians.</param>
/// <returns><see cref="CoordinatePoint" /> at specified distance and direction from the base point.</returns>
/// <seealso cref="http://www.movable-type.co.uk/scripts/latlong.html"/>
public static CoordinatePoint GetCoordinatePointAtDistanceAndDirectionWithHaversine(CoordinatePoint basePoint, LinearDimension distance, double azimuth, out double backAzimuth)
{
var startLatitudeRadians = basePoint.Latitude.ToRadians();
var dR = distance.GetMeters() / _earthWgs84MeanRadius;
var finishLatitudeRadians = Math.Asin(Math.Sin(startLatitudeRadians) * Math.Cos(dR) +
Math.Cos(startLatitudeRadians) * Math.Sin(dR) * Math.Cos(azimuth));
var finishLongitudeRadians = basePoint.Longitude.ToRadians() +
Math.Atan2(Math.Sin(azimuth) * Math.Sin(dR) * Math.Cos(startLatitudeRadians), Math.Cos(dR) - Math.Sin(startLatitudeRadians) * Math.Sin(finishLatitudeRadians));
var y = Math.Sin(finishLongitudeRadians - basePoint.Longitude.ToRadians()) * Math.Cos(finishLatitudeRadians);
var x = Math.Cos(startLatitudeRadians) * Math.Sin(finishLatitudeRadians) -
Math.Sin(startLatitudeRadians) * Math.Cos(finishLatitudeRadians) * Math.Cos(finishLongitudeRadians - basePoint.Longitude.ToRadians());
backAzimuth = Math.Atan2(y, x) + Math.PI;
return(new CoordinatePoint(Latitude.FromRadians(finishLatitudeRadians), Longitude.FromRadians(finishLongitudeRadians)));
}
