/// <summary>
/// Find the point that is the given distance from the start point in the direction of the end point.
/// The distance must be less than the distance between these two points.
/// </summary>
/// <param name="start">Start Geography Point</param>
/// <param name="end">End Geography Point</param>
/// <param name="distance">Distance at which the point to be located</param>
/// <returns></returns>
public static SqlGeography InterpolateBetweenGeog(SqlGeography start, SqlGeography end, double distance)
{
// We need to check a few prerequisite.
// We only operate on points.
if (!start.IsPoint() || !end.IsPoint())
{
throw new ArgumentException(ErrorMessage.PointCompatible);
}
// The SRIDs also have to match
var srid = start.STSrid.Value;
if (srid != end.STSrid.Value)
{
throw new ArgumentException(ErrorMessage.SRIDCompatible);
}
// Finally, the distance has to fall between these points.
var length = start.STDistance(end).Value;
if (distance > length)
{
throw new ArgumentException(ErrorMessage.DistanceMustBeBetweenTwoPoints);
}
if (distance < 0)
{
throw new ArgumentException(ErrorMessage.DistanceMustBePositive);
}
// We'll just do this by binary search---surely this could be more efficient,
// but this is relatively easy.
//
// Note that we can't just take the take the linear combination of end vectors because we
// aren't working on a sphere.
// We are going to do our binary search using 3D Cartesian values, however
var startCart = SpatialUtil.GeographicToCartesian(start);
var endCart = SpatialUtil.GeographicToCartesian(end);
SqlGeography current;
double currentDistance;
// Keep refining until we slip below the THRESHOLD value.
do
{
var currentCart = (startCart + endCart) / 2;
current = SpatialUtil.CartesianToGeographic(currentCart, srid);
currentDistance = start.STDistance(current).Value;
if (distance <= currentDistance)
{
endCart = currentCart;
}
else
{
startCart = currentCart;
}
} while (Math.Abs(currentDistance - distance) > Constants.Tolerance);
return(current);
}
