/// <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));
}
