/// <summary>
/// Calculates the position of the Sun on the Ecliptic for the given Julian Day
/// </summary>
/// <param name="n">The Julian Day</param>
/// <returns>The position of the sun on the ecliptic</returns>
public static GeocentricEclipticSphericalPosition ToGeocentricEclipticSphericalFromJulianDay(this float n)
{
var L_deg = (280.460f + (0.9856474f * n)).Repeat(360f);
var g_deg = (357.528f + (0.9856003f * n)).Repeat(360f);
var g_rad = Degrees.Radians(g_deg);
var sin_g = Sin(g_rad);
var cos_g = Cos(g_rad);
var lambda_deg = ((float)(L_deg + (1.915f * sin_g) + (0.020f * 2 * sin_g * cos_g))).Repeat(360);
var R = 1.00014f - (0.01671f * cos_g) - (0.00014f * ((cos_g * cos_g) - (sin_g * sin_g)));
var ec = new GeocentricEclipticSphericalPosition(0, lambda_deg, (float)R);
return(ec);
}
/// <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));
}
/// <summary>
/// Converts this LatLngPoint to a Universal Transverse Mercator 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.
/// </summary>
/// <seealso cref="http://www.uwgb.edu/dutchs/usefuldata/utmformulas.htm"/>
/// <param name="latlng">The point on Earth to convert to UTM</param>
/// <returns>The UTM point</returns>
public static UTMPoint ToUTM(this LatLngPoint latlng)
{
if (latlng is null)
{
throw new ArgumentNullException(nameof(latlng));
}
var hemisphere = latlng.Latitude < 0
? UTMPoint.GlobeHemisphere.Southern
: UTMPoint.GlobeHemisphere.Northern;
const double k0 = 0.9996;
double phi = Degrees.Radians(latlng.Latitude);
var sinPhi = Sin(phi);
var cosPhi = Cos(phi);
var sin2Phi = 2 * sinPhi * cosPhi;
var cos2Phi = (2 * cosPhi * cosPhi) - 1;
var sin4Phi = 2 * sin2Phi * cos2Phi;
var cos4Phi = (2 * cos2Phi * cos2Phi) - 1;
var sin6Phi = (sin4Phi * cos2Phi) + (cos4Phi * sin2Phi);
var tanPhi = sinPhi / cosPhi;
var ePhi = DatumWGS_84.e * sinPhi;
var N = DatumWGS_84.equatorialRadius / Sqrt(1 - (ePhi * ePhi));
var utmz = 1 + (int)Floor((latlng.Longitude + 180) / 6.0);
var zcm = 3 + (6.0 * (utmz - 1)) - 180;
var A = Degrees.Radians((float)(latlng.Longitude - zcm)) * cosPhi;
var M = DatumWGS_84.equatorialRadius * (
(phi * DatumWGS_84.alpha1)
- (sin2Phi * DatumWGS_84.alpha2)
+ (sin4Phi * DatumWGS_84.alpha3)
- (sin6Phi * DatumWGS_84.alpha4));
// Easting
var T = tanPhi * tanPhi;
var C = DatumWGS_84.e0sq * cosPhi * cosPhi;
var Asqr = A * A;
var Tsqr = T * T;
var x0 = 1 - T + C;
var x1 = 5 - (18 * T) + Tsqr + (72.0 * C) - (58 * DatumWGS_84.e0sq);
var x2 = Asqr * x1 / 120.0;
var x3 = (x0 / 6) + x2;
var x4 = 1 + (Asqr * x3);
var easting = k0 * N * A * x4;
easting += DatumWGS_84.E0;
// Northing
var northing = k0 * (M + (N * tanPhi * (Asqr * ((1 / 2.0) + (Asqr * (((5 - T + (9 * C) + (4 * C * C)) / 24.0) + (Asqr * (61 - (58 * T) + Tsqr + (600 * C) - (330 * DatumWGS_84.e0sq)) / 720.0)))))));
if (hemisphere == UTMPoint.GlobeHemisphere.Southern)
{
northing += DatumWGS_84.FalseNorthing;
}
return(new UTMPoint(
(float)easting,
(float)northing,
latlng.Altitude,
utmz,
hemisphere));
}