/// <summary>
/// Provides a quick calculation of a pseudo distance to another
/// point that can be used when find nearest positions.
/// Based on Equirrectangular approximation but without the radius and Sqrt calculation.
/// </summary>
/// <param name="to"></param>
/// <param name="radius"></param>
/// <returns></returns>
public double OrderingDistanceTo(LatLongCoordinate to)
{
/*
* Taken from: http://www.movable-type.co.uk/scripts/latlong.html
* Formula x = Δλ ⋅ cos φm
* y = Δφ
* d = R ⋅ √x² + y²
* JavaScript:
* var x = (λ2-λ1) * Math.cos((φ1+φ2)/2);
* var y = (φ2-φ1);
* var d = Math.sqrt(x*x + y*y) * R;
*/
double theta1 = this.Latitude.Radians; // Equivalent to φ1
double theta2 = to.Latitude.Radians; // Equivalent to φ2
double deltaTheta = theta2 - theta1; // eqivalent to Δφ
double deltaGamma = to.Longitude.Radians - this.Longitude.Radians; // equivalent to Δλ
double x = deltaGamma * Math.Cos((theta1 + theta2) / 2);
double d = Math.Pow(x, 2) + Math.Pow(deltaTheta, 2);
return(d);
}
/// <summary>
/// Calculates the great circle distance to another point assuming
/// both points at a given radial distance.
/// </summary>
/// <param name="toCoordinate"></param>
/// <returns></returns>
public double DistanceTo(LatLongCoordinate to, double radius)
{
/*
* Taken from: http://www.movable-type.co.uk/scripts/latlong.html
* Haversine
* formula: 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 (mean radius = 6,371km);
* note that angles need to be in radians to pass to trig functions!
* JavaScript:
* var R = 6371e3; // metres
* var φ1 = lat1.toRadians();
* var φ2 = lat2.toRadians();
* var Δφ = (lat2-lat1).toRadians();
* var Δλ = (lon2-lon1).toRadians();
*
* var a = Math.sin(Δφ/2) * Math.sin(Δφ/2) +
* Math.cos(φ1) * Math.cos(φ2) *
* Math.sin(Δλ/2) * Math.sin(Δλ/2);
* var c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a));
*
* var d = R * c;
*/
double theta1 = this.Latitude.Radians; // Equivalent to φ1
double theta2 = to.Latitude.Radians; // Equivalent to φ2
double deltaTheta = theta2 - theta1; // eqivalent to Δφ
double deltaGamma = to.Longitude.Radians - this.Longitude.Radians; // equivalent to Δλ
double a = Math.Pow(Math.Sin(deltaTheta / 2), 2) +
Math.Cos(theta1) * Math.Cos(theta2) *
Math.Pow(Math.Sin(deltaGamma), 2);
double c = 2 * Math.Atan2(Math.Sqrt(a), Math.Sqrt(1 - a));
double d = radius * c;
return(d);
}
