/// <summary>
/// Forward projection, from geographic to Cassini-Soldner.
/// </summary>
/// <param name="lat">latitude of point (degrees).</param>
/// <param name="lon">longitude of point (degrees).</param>
/// <param name="azi">azimuth of easting direction at point (degrees).</param>
/// <param name="rk">reciprocal of azimuthal northing scale at point.</param>
/// <returns>
/// <i>x</i>, easting of point and <i>y</i>, northing of point, in meters.
/// </returns>
/// <remarks>
/// <paramref name="lat"/> should be in the range [−90°, 90°].
/// A call to <see cref="Forward(double, double, out double, out double)"/>
/// followed by a call to <see cref="Reverse(double, double, out double, out double)"/>
/// will return the original (<paramref name="lat"/>, <paramref name="lon"/>) (to within roundoff).
/// The routine does nothing if the origin has not been set.
/// </remarks>
public (double x, double y) Forward(double lat, double lon, out double azi, out double rk)
{
var dlon = AngDiff(LongitudeOrigin, lon);
var sig12 =
_earth.Inverse(lat, -Abs(dlon), lat, Abs(dlon), out var s12, out var azi1, out var azi2);
sig12 *= 0.5;
s12 *= 0.5;
if (s12 == 0)
{
var da = AngDiff(azi1, azi2) / 2;
if (Abs(dlon) <= 90)
{
azi1 = 90 - da;
azi2 = 90 + da;
}
else
{
azi1 = -90 - da;
azi2 = -90 + da;
}
}
if (dlon < 0)
{
azi2 = azi1;
s12 = -s12;
sig12 = -sig12;
}
var x = s12;
azi = AngNormalize(azi2);
var perp = _earth.Line(lat, dlon, azi, GeodesicFlags.GeodesicScale);
perp.GenPosition(true, -sig12,
GeodesicFlags.GeodesicScale,
out _, out _, out _, out _, out _, out _, out rk, out _);
SinCosd(perp.EquatorialAzimuth, out var salp0, out var calp0);
double
sbet1 = lat >= 0 ? calp0 : -calp0,
cbet1 = Abs(dlon) <= 90 ? Abs(salp0) : -Abs(salp0),
sbet01 = sbet1 * _cbet0 - cbet1 * _sbet0,
cbet01 = cbet1 * _cbet0 + sbet1 * _sbet0,
sig01 = Atan2(sbet01, cbet01) / Degree;
_meridian.GenPosition(true, sig01,
GeodesicFlags.Distance,
out _, out _, out _, out var y, out _, out _, out _, out _);
return(x, y);
}
