/// <summary>
/// Compute the meridian convergence for a location
/// </summary>
/// <param name="point">The location defined by latitude/longitude</param>
/// <returns>The meridian convergence</returns>
public Angle MeridianConvergence(GlobalCoordinates point)
{
double scaleFactor;
double meridianConvergence;
var c = ToUtmCoordinates(point, out scaleFactor, out meridianConvergence);
return(Angle.RadToDeg(meridianConvergence));
}
/// <summary>
/// Convert the Y coordinate (in meters) on a Mercator map back into the longitude
/// </summary>
/// <param name="y">The Y coordinate (in meters) on a Mercator map</param>
/// <returns>The longitude (in degrees)</returns>
public override double YToLatitude(double y)
{
var ts = Math.Exp(-y / ReferenceGlobe.SemiMajorAxis);
var phi = 0.5 * Math.PI - 2.0 * Math.Atan(ts);
var dphi = 1.0;
var i = 0;
while ((Math.Abs(dphi) > 0.000000001) && (i < 15))
{
var con = ReferenceGlobe.Eccentricity * Math.Sin(phi);
dphi = 0.5 * Math.PI -
2.0 * Math.Atan(ts * Math.Pow((1.0 - con) / (1.0 + con), 0.5 * ReferenceGlobe.Eccentricity)) - phi;
phi += dphi;
i++;
}
var d = Angle.RadToDeg(phi);
return(NormalizeLatitude(d).Degrees);
}
/// <summary>
/// Convert the X coordinate (in meters) on a Mercator map back into the longitude
/// </summary>
/// <param name="x">The X coordinate (in meters) on a Mercator map</param>
/// <returns>The longitude (in degrees)</returns>
public double XToLongitude(double x)
{
var longitude = ReferenceMeridian + Angle.RadToDeg(x / ReferenceGlobe.SemiMajorAxis);
return(NormalizeLongitude(longitude).Degrees);
}
/// <summary>
/// Compute the meridian convergence for a location
/// </summary>
/// <param name="point">The location defined by latitude/longitude</param>
/// <returns>The meridian convergence</returns>
public Angle MeridianConvergence(GlobalCoordinates point)
{
ToUtmCoordinates(point, out _, out var meridianConvergence);
return(Angle.RadToDeg(meridianConvergence));
}
internal GlobalCoordinates FromEuclidian(
EuclidianCoordinate xy,
out double scaleFactor,
out double meridianConvergence)
{
if (!(xy is UtmCoordinate point))
{
throw new ArgumentException(Properties.Resource.NO_UTM_COORDINATE);
}
var hemi = point.Grid.IsNorthern ? 1 : -1;
var northingOffset = point.Grid.IsNorthern ? 0.0 : Southern_Northing_Offset;
var chi = (point.Y - northingOffset) / (MathConsts.K0 * _m.A);
var eta = (point.X - MathConsts.E0) / (MathConsts.K0 * _m.A);
var sum = 0.0;
for (var j = 1; j <= 3; j++)
{
sum += (_m.Beta[j - 1] * Math.Sin(2.0 * j * chi) * Math.Cosh(2.0 * j * eta));
}
var chitick = chi - sum;
sum = 0.0;
for (var j = 1; j <= 3; j++)
{
sum += (_m.Beta[j - 1] * Math.Cos(2.0 * j * chi) * Math.Sinh(2.0 * j * eta));
}
var etatick = eta - sum;
sum = 0.0;
for (var j = 1; j <= 3; j++)
{
sum += (2.0 * j * _m.Beta[j - 1] * Math.Cos(2.0 * j * chi) * Math.Cosh(2.0 * j * eta));
}
var sigmatick = 1.0 - sum;
var tautick = 0.0;
for (var j = 1; j <= 3; j++)
{
tautick += (2.0 * j * _m.Beta[j - 1] * Math.Sin(2.0 * j * chi) * Math.Sinh(2.0 * j * eta));
}
var xi = Math.Asin(Math.Sin(chitick) / Math.Cosh(etatick));
var phi = xi;
for (var j = 1; j <= 3; j++)
{
phi += (_m.Delta[j - 1] * Math.Sin(2.0 * j * xi));
}
var lambda0 = point.Grid.CenterMeridian.Radians;
var lambda = lambda0 + Math.Atan(Math.Sinh(etatick) / Math.Cos(chitick));
var k = ((MathConsts.K0 * _m.A) / ReferenceGlobe.SemiMajorAxis) *
Math.Sqrt(((Math.Pow(Math.Cos(chitick), 2.0) + Math.Pow(Math.Sinh(etatick), 2.0)) /
(sigmatick * sigmatick + tautick * tautick)) *
(1.0 + Math.Pow(((1.0 - _m.N) / (1.0 + _m.N)) * Math.Tan(phi), 2.0)));
var gamma = Math.Atan((tautick + sigmatick * Math.Tan(chitick) * Math.Tanh(etatick)) /
(sigmatick - tautick * Math.Tan(chitick) * Math.Tanh(etatick))) * hemi;
scaleFactor = k;
meridianConvergence = gamma;
return(new GlobalCoordinates(Angle.RadToDeg(phi), Angle.RadToDeg(lambda)));
}
/// <summary>
/// Convert the Y coordinate (in meters) on a Mercator map back into the longitude
/// </summary>
/// <param name="y">The Y coordinate (in meters) on a Mercator map</param>
/// <returns>The longitude (in degrees)</returns>
public override double YToLatitude(double y)
{
var latitude = Angle.RadToDeg(2.0 * Math.Atan(Math.Exp(y / ReferenceGlobe.SemiMajorAxis)) - 0.5 * Math.PI);
return(NormalizeLatitude(latitude).Degrees);
}