/// <summary>
/// Let first point latitude be la1,
/// longitude as lo1,
/// d be distance,
/// R as radius of Earth,
/// Ad be the angular distance i.e d/R and
/// θ be the bearing,
/// Here is the formula to find the second point, when first point, bearing and distance is known:
/// latitude of second point = la2 = asin(sin la1 * cos Ad + cos la1 * sin Ad * cos θ), and
/// longitude of second point = lo2 = lo1 + atan2(sin θ * sin Ad * cos la1, cos Ad – sin la1 * sin la2)
/// </summary>
/// <param name="oldLatitude"></param>
/// <param name="oldLongitude"></param>
/// <param name="bearing"></param>
/// <param name="distance"></param>
/// <returns>New set of latitude and longitude points</returns>
public static (double, double) CalculateNewSetOfPoints(
double oldLatitude, double oldLongitude,
double bearing, double distance)
{
oldLatitude = HaversineFormula.ConvertDegreesToRadians(oldLatitude);
oldLongitude = HaversineFormula.ConvertDegreesToRadians(oldLongitude);
double Ad = distance / R;
double newLatitude = Math.Asin(Math.Sin(oldLatitude) * Math.Cos(Ad) + Math.Cos(oldLatitude) * Math.Sin(Ad) * Math.Cos(bearing));
double newLongitude = oldLongitude + Math.Atan2(Math.Sin(bearing) * Math.Sin(Ad) * Math.Cos(oldLatitude), Math.Cos(Ad) - Math.Sin(oldLatitude) * Math.Sin(newLatitude));
return(Math.Round(HaversineFormula.ConvertRadiansToDegrees(newLatitude), 8), Math.Round(HaversineFormula.ConvertRadiansToDegrees(newLongitude), 8));
}
/// <summary>
/// a = sin²(Δφ/2) + cos φ1 ⋅ cos φ2 ⋅ sin²(Δλ/2)
/// c = 2 ⋅ atan2( √a, √(1−a) )
/// d = R ⋅ c
/// where φ is latitude, λ is longitude, R is earth’s radius
/// note that angles need to be in radians to pass to trig functions!
/// </summary>
/// <param name="firstLatitude"></param>
/// <param name="firstLongitude"></param>
/// <param name="secondLatitude"></param>
/// <param name="secondLongidute"></param>
/// <returns>Distance between chosen points</returns>
public static double CalculateDistanceBetweenTwoPoints(
double firstLatitude, double firstLongitude,
double secondLatitude, double secondLongidute)
{
firstLatitude = HaversineFormula.ConvertDegreesToRadians(firstLatitude);
firstLongitude = HaversineFormula.ConvertDegreesToRadians(firstLongitude);
secondLatitude = HaversineFormula.ConvertDegreesToRadians(secondLatitude);
secondLongidute = HaversineFormula.ConvertDegreesToRadians(secondLongidute);
double a = 0.5 - Math.Cos(secondLatitude - firstLatitude) / 2 + Math.Cos(firstLatitude) * Math.Cos(secondLatitude) * (1 - Math.Cos(secondLongidute - firstLongitude)) / 2;
// ili 2*R*Math.atan2(sqrt(a), sqrt(1-a));
return(2 * R * Math.Asin(Math.Sqrt(a)));
}
/// <summary>
/// Bearing: The horizontal angle at a given point, measured clockwise from magnetic north or true north to a second point.
/// Let ‘R’ be the radius of Earth,
/// ‘L’ be the longitude,
/// ‘θ’ be latitude,
/// ‘β‘ be Bearing.
/// Bearing from point A to B, can be calculated as,
/// β = atan2(X, Y),
/// where, X and Y are two quantities and can be calculated as:
/// X = cos θb* sin ∆L
/// Y = cos θa* sin θb – sin θa * cos θb * cos ∆L
/// </summary>
/// <param name="firstLatitude"></param>
/// <param name="firstLongitude"></param>
/// <param name="secondLatitude"></param>
/// <param name="secondLongidute"></param>
/// <returns>Bearing from first to second point</returns>
public static double Bearing(
double firstLatitude, double firstLongitude,
double secondLatitude, double secondLongidute)
{
firstLatitude = HaversineFormula.ConvertDegreesToRadians(firstLatitude);
firstLongitude = HaversineFormula.ConvertDegreesToRadians(firstLongitude);
secondLatitude = HaversineFormula.ConvertDegreesToRadians(secondLatitude);
secondLongidute = HaversineFormula.ConvertDegreesToRadians(secondLongidute);
double firstPoint = Math.Cos(secondLatitude) * Math.Sin(secondLongidute - firstLongitude);
double secondPoint = (Math.Cos(firstLatitude) * Math.Sin(secondLatitude)) - (Math.Sin(firstLatitude) * Math.Cos(secondLatitude) * Math.Cos(secondLongidute - firstLongitude));
return(Math.Atan2(firstPoint, secondPoint));
}
public static IEnumerable <(double, double)> MoveAtRoute(
double firstLatitude, double firstLongitude,
double secondLatitude, double secondLongidute,
double stepLengthToMove, double precisionOfStep)
{
firstLatitude = HaversineFormula.ConvertDegreesToRadians(firstLatitude);
firstLongitude = HaversineFormula.ConvertDegreesToRadians(firstLongitude);
secondLatitude = HaversineFormula.ConvertDegreesToRadians(secondLatitude);
secondLongidute = HaversineFormula.ConvertDegreesToRadians(secondLongidute);
IList <(double, double)> newLatLng = new List <(double, double)>();
while (HaversineFormula.CalculateDistanceBetweenTwoPoints(
firstLatitude, firstLongitude,
secondLatitude, secondLongidute) > precisionOfStep)
{
double bearing = HaversineFormula.Bearing(firstLatitude, firstLongitude,
secondLatitude, secondLongidute);
newLatLng.Add(HaversineFormula.CalculateNewSetOfPoints(firstLatitude, firstLongitude, bearing, precisionOfStep));
}
return(newLatLng);
}