/// <summary>
/// Calculate how far the point is along a track from the start-point, heading towards the end-point.
/// <para>That is, if a perpendicular is drawn from the point to the (great circle) path, the along-track distance is the distance from the start point to where the perpendicular crosses the path.</para>
/// </summary>
/// <param name="pointA">The point to calculate the distance from.</param>
/// <param name="startPoint">Start point of great circle path.</param>
/// <param name="endPoint">End point of great circle path.</param>
/// <param name="radius">Radius of earth.</param>
/// <returns>The distance along great circle to point nearest point A in the same units as the radius.</returns>
public double AlongTrackDistance(ICoordinate pointA, ICoordinate startPoint, ICoordinate endPoint, double radius)
{
if (pointA == null)
{
throw new ArgumentNullException(nameof(pointA), "The argument cannot be null.");
}
if (startPoint == null)
{
throw new ArgumentNullException(nameof(startPoint), "The argument cannot be null.");
}
if (endPoint == null)
{
throw new ArgumentNullException(nameof(endPoint), "The argument cannot be null.");
}
ValidateRadius(radius);
var δ13 = startPoint.DistanceTo(pointA, radius) / radius;
var θ13 = startPoint.BearingTo(pointA).ToRadians();
var θ12 = startPoint.BearingTo(endPoint).ToRadians();
var δxt = Math.Asin(Math.Sin(δ13) * Math.Sin(θ13 - θ12));
var δat = Math.Acos(Math.Cos(δ13) / Math.Abs(Math.Cos(δxt)));
var result = δat * Math.Sign(Math.Cos(θ12 - θ13)) * radius;
return(result);
}
/// <summary>
/// Calculate final bearing arriving at destination point from point A.
/// <para>The final bearing will differ from the initial bearing by varying degrees according to distance and latitude.</para>
/// </summary>
/// <param name="pointA">The start point.</param>
/// <param name="pointB">The end point.</param>
/// <returns>Final bearing in degrees from north.</returns>
public double FinalBearing(ICoordinate pointA, ICoordinate pointB)
{
if (pointA == null)
{
throw new ArgumentNullException(nameof(pointA), "The argument cannot be null.");
}
if (pointB == null)
{
throw new ArgumentNullException(nameof(pointB), "The argument cannot be null.");
}
// Get initial bearing from destination point to this point & reverse it by adding 180°.
var result = (pointB.BearingTo(pointA) + 180) % 360;
return(result);
}
