private static LatitudeLongtitude CalculateAiry1830(OSGB36 coordinates, double latitude,
double transverseRadiusOfCurvature, double eccentricitySquared)
{
var meridionalRadiusOfCurvature = Airy180SemiMajorAxis * ScaleFactorOnCentralMeridian * (1 - eccentricitySquared) * Math.Pow((1 - (eccentricitySquared * latitude.SinToPower(2))), -1.5);
var eta2 = (transverseRadiusOfCurvature / meridionalRadiusOfCurvature) - 1;
var secLat = 1.0 / Math.Cos(latitude);
var vii = Math.Tan(latitude) / (2 * meridionalRadiusOfCurvature * transverseRadiusOfCurvature);
var viii = Math.Tan(latitude) / (24 * meridionalRadiusOfCurvature * Math.Pow(transverseRadiusOfCurvature, 3)) *
(5 + 3 * latitude.TanToPower(2) + eta2 - 9 * latitude.TanToPower(2) * eta2);
var ix = Math.Tan(latitude) / (720 * meridionalRadiusOfCurvature * Math.Pow(transverseRadiusOfCurvature, 5)) *
(61 + 90 * latitude.TanToPower(2) + 45 * latitude.TanToPower(4));
var x = secLat / transverseRadiusOfCurvature;
var xi = secLat / (6 * Math.Pow(transverseRadiusOfCurvature, 3)) *
(transverseRadiusOfCurvature / meridionalRadiusOfCurvature + 2 * latitude.TanToPower(2));
var xii = secLat / (120 * Math.Pow(transverseRadiusOfCurvature, 5)) *
(5 + 28 * latitude.TanToPower(2) + 24 * latitude.TanToPower(4));
var xiia = secLat / (5040 * Math.Pow(transverseRadiusOfCurvature, 7)) *
(61 + 662 * latitude.TanToPower(2) + 1320 * latitude.TanToPower(4) + 720 * latitude.TanToPower(6));
var eastingDifference = coordinates.Easting - EastingOfTrueOrigin;
return(new LatitudeLongtitude {
Latitude = latitude - vii * Math.Pow(eastingDifference, 2) + viii * Math.Pow(eastingDifference, 4) -
ix * Math.Pow(eastingDifference, 6),
Longtitude = LongtitudeOfTrueOrigin + x * eastingDifference - xi * Math.Pow(eastingDifference, 3) +
xii * Math.Pow(eastingDifference, 5) - xiia * Math.Pow(eastingDifference, 7)
});
}
public static WGS84 Convert(OSGB36 coordinates)
{
var latitude = InitializeLatitude(coordinates);
var grs80 = CalculateGrs80(coordinates, latitude);
latitude = RecalculateLatitude(grs80);
return(new WGS84 {
Latitude = latitude * 180 / Math.PI,
Longtitude = Math.Atan2(grs80.Y, grs80.X) * 180 / Math.PI
});
}
private static Cartesian CalculateGrs80(OSGB36 coordinates, double latitude)
{
var eccentricitySquared = 1 - (Math.Pow(Airy180SemiMinorAxis, 2) / Math.Pow(Airy180SemiMajorAxis, 2));
var transverseRadiusOfCurvature = Airy180SemiMajorAxis * ScaleFactorOnCentralMeridian /
Math.Sqrt(1 - (eccentricitySquared * latitude.SinToPower(2)));
var airy1830 = CalculateAiry1830(coordinates, latitude, transverseRadiusOfCurvature, eccentricitySquared);
var cartesian = new Cartesian {
X = (transverseRadiusOfCurvature / ScaleFactorOnCentralMeridian) * Math.Cos(airy1830.Latitude) * Math.Cos(airy1830.Longtitude),
Y = (transverseRadiusOfCurvature / ScaleFactorOnCentralMeridian) * Math.Cos(airy1830.Latitude) * Math.Sin(airy1830.Longtitude),
Z = ((1 - eccentricitySquared) * transverseRadiusOfCurvature / ScaleFactorOnCentralMeridian) * Math.Sin(airy1830.Latitude)
};
var grs80 = new Cartesian {
X = 446.448 + (1 + ScaleFactor) * cartesian.X - ZRadians * cartesian.Y + YRadians * cartesian.Z,
Y = -125.157 + ZRadians * cartesian.X + (1 + ScaleFactor) * cartesian.Y - XRadians * cartesian.Z,
Z = 542.060 - YRadians * cartesian.X + XRadians * cartesian.Y + (1 + ScaleFactor) * cartesian.Z
};
return(grs80);
}
private static double InitializeLatitude(OSGB36 coordinates)
{
var latitude = LatitudeOfTrueOrigin;
var meridionalArc = 0.0;
while (coordinates.Northing - NorthingOfTrueOrigin - meridionalArc >= 0.00001)
{
latitude += (coordinates.Northing - NorthingOfTrueOrigin - meridionalArc) /
(Airy180SemiMajorAxis * ScaleFactorOnCentralMeridian);
var meridionalArc1 = (1.0 + N + (1.25 * Math.Pow(N, 2)) + (1.25 * Math.Pow(N, 3))) *
(latitude - LatitudeOfTrueOrigin);
var meridionalArc2 = ((3 * N) + (3 * Math.Pow(N, 2)) + ((21.0 / 8) * Math.Pow(N, 3))) *
Math.Sin(latitude - LatitudeOfTrueOrigin) *
Math.Cos(latitude + LatitudeOfTrueOrigin);
var meridionalArc3 = ((15.0 / 8) * Math.Pow(N, 2) + (15.0 / 8) * Math.Pow(N, 3)) *
Math.Sin(2 * (latitude - LatitudeOfTrueOrigin)) *
Math.Cos(2 * (latitude + LatitudeOfTrueOrigin));
var meridionalArc4 = (35.0 / 24) * Math.Pow(N, 3) * Math.Sin(3 * (latitude - LatitudeOfTrueOrigin)) *
Math.Cos(3 * (latitude + LatitudeOfTrueOrigin));
meridionalArc = Airy180SemiMinorAxis * ScaleFactorOnCentralMeridian *
(meridionalArc1 - meridionalArc2 + meridionalArc3 - meridionalArc4);
}
return(latitude);
}
