/// <summary>
/// Converts this UTMPoint to a Latitude/Longitude point using the WGS-84 datum. The
/// coordinate pair's units will be in meters, and should be usable to make distance
/// calculations over short distances. /// reference: http://www.uwgb.edu/dutchs/usefuldata/utmformulas.htm
/// </summary>
/// <param name="utm">The UTM point to convert</param>
/// <returns>The latitude/longitude</returns>
public static LatLngPoint ToLatLng(this UTMPoint utm)
{
if (utm is null)
{
throw new ArgumentNullException(nameof(utm));
}
var N0 = utm.Hemisphere == UTMPoint.GlobeHemisphere.Northern ? 0.0 : DatumWGS_84.FalseNorthing;
var xi = (utm.Y - N0) / (DatumWGS_84.pointScaleFactor * DatumWGS_84.A);
var eta = (utm.X - DatumWGS_84.E0) / (DatumWGS_84.pointScaleFactor * DatumWGS_84.A);
var xiPrime = xi;
var etaPrime = eta;
double sigmaPrime = 1;
double tauPrime = 0;
for (var j = 1; j <= 3; ++j)
{
var beta = DatumWGS_84.beta[j - 1];
var je2 = 2 * j * xi;
var jn2 = 2 * j * eta;
var sinje2 = Sin(je2);
var coshjn2 = Cosh(jn2);
var cosje2 = Cos(je2);
var sinhjn2 = Sinh(jn2);
xiPrime -= beta * sinje2 * coshjn2;
etaPrime -= beta * cosje2 * sinhjn2;
sigmaPrime -= 2 * j * beta * cosje2 * coshjn2;
tauPrime -= 2 * j * beta * sinje2 * sinhjn2;
}
var chi = Asin(Sin(xiPrime) / Cosh(etaPrime));
var lat = chi;
for (var j = 1; j <= 3; ++j)
{
lat += DatumWGS_84.delta[j - 1] * Sin(2 * j * chi);
}
float long0 = (utm.Zone * 6) - 183;
var lng = Atan(Sinh(etaPrime) / Cos(xiPrime));
return(new LatLngPoint(
Radians.Degrees((float)lat),
long0 + Radians.Degrees((float)lng),
utm.Z));
}
/// <summary>
/// Convert Equitorial Spherical Position to Horizontal Spherical Position.
/// </summary>
/// <param name="location">The point on earth</param>
/// <param name="n">The Julian day</param>
/// <returns>The elevation above the horizon</returns>
public static HorizontalSphericalPosition ToHorizontal(this EquitorialSphericalPosition value, LatLngPoint location, float n)
{
if (value is null)
{
throw new ArgumentNullException(nameof(value));
}
if (location is null)
{
throw new ArgumentNullException(nameof(location));
}
var GMST = (18.697374558f + (24.06570982441908f * n)).Repeat(24);
var LST = GMST + Degrees.Hours(location.Longitude);
var RA = Degrees.Hours(value.RightAscensionDegrees);
var H = Hours.Radians(LST - RA);
var sin_H = Sin(H);
var cos_H = Cos(H);
var lat_rad = Degrees.Radians(location.Latitude);
// var lng_rad = lng_deg * Deg2Rad;
var delta_rad = Degrees.Radians(value.DeclinationDegrees);
var sin_delta = Sin(delta_rad);
var cos_delta = Cos(delta_rad);
var sin_lat = Sin(lat_rad);
var cos_lat = Cos(lat_rad);
var sin_alt = (sin_delta * sin_lat) + (cos_delta * cos_lat * cos_H);
var cos_alt = Sqrt(1 - (sin_alt * sin_alt));
var sin_azm = sin_H * cos_delta / cos_alt;
var cos_azm = (sin_delta - (sin_lat * sin_alt)) / (cos_lat * cos_alt);
var altitude_rad = (float)Atan2(sin_alt, cos_alt);
var azimuth_rad = (float)Atan2(sin_azm, cos_azm);
return(new HorizontalSphericalPosition(
Radians.Degrees(altitude_rad),
(180 - Radians.Degrees(azimuth_rad)).Repeat(360),
value.RadiusAU));
}
/// <summary>
/// This calculation is only good for the Sun, as it does not take the Ecliptic Latitude into consideration.
/// </summary>
/// <param name="n">The Julian Day</param>
/// <returns>The position of the son on the equitorial plane</returns>
public static EquitorialSphericalPosition ToEquitorial(this GeocentricEclipticSphericalPosition p, float n)
{
if (p is null)
{
throw new ArgumentNullException(nameof(p));
}
var epsilon_deg = 23.439f - (0.0000004f * n);
var epsilon_rad = Degrees.Radians(epsilon_deg);
var sin_epsilon = Sin(epsilon_rad);
var cos_epsilon = Cos(epsilon_rad);
var lambda_rad = Degrees.Radians(p.LongitudeDegrees);
var sin_lambda = Sin(lambda_rad);
var cos_lambda = Cos(lambda_rad);
var alpha_rad = (float)Atan2(cos_epsilon * sin_lambda, cos_lambda);
var delta_rad = (float)Asin(sin_epsilon * sin_lambda);
return(new EquitorialSphericalPosition(
Radians.Degrees(alpha_rad),
Radians.Degrees(delta_rad),
p.RadiusAU));
}