/// <summary>
/// Forward projection, from geographic to gnomonic.
/// </summary>
/// <param name="lat0">latitude of center point of projection (degrees).</param>
/// <param name="lon0">longitude of center point of projection (degrees).</param>
/// <param name="lat">latitude of point (degrees).</param>
/// <param name="lon">longitude of point (degrees).</param>
/// <param name="azi">azimuth of geodesic at point (degrees).</param>
/// <param name="rk">reciprocal of azimuthal scale at point.</param>
/// <returns>
/// <i>x</i>, easting of point (meters) and <i>y</i>, northing of point (meters).
/// </returns>
/// <remarks>
/// <paramref name="lat0"/> and <paramref name="lat"/> should be in the range [−90°, 90°].
/// The scale of the projection is 1/<paramref name="rk"/>^2 in the "radial" direction, <paramref name="azi"/> clockwise from true north,
/// and is 1/<paramref name="rk"/> in the direction perpendicular to this. If the point lies "over the horizon", i.e.,
/// if <paramref name="rk"/> ≤ 0, then <see cref="double.NaN"/>s are returned for <i>x</i> and <i>y</i>
/// (the correct values are returned for <paramref name="azi"/> and <paramref name="rk"/>).
/// A call to <see cref="Forward(double, double, double, double, out double, out double)"/> followed by a call to
/// <see cref="Reverse(double, double, double, double, out double, out double)"/> will return the
/// original (<paramref name="lat"/>, <paramref name="lon"/>) (to within roundoff) provided the point in not over the horizon.
/// </remarks>
public (double x, double y) Forward(double lat0, double lon0, double lat, double lon, out double azi, out double rk)
{
double x, y;
_earth.GenInverse(lat0, lon0, lat, lon,
GeodesicFlags.Azimuth | GeodesicFlags.ReducedLength | GeodesicFlags.GeodesicScale,
out _, out var azi0, out azi, out var m, out var M, out _, out _);
rk = M;
if (M <= 0)
{
x = y = double.NaN;
}
else
{
var rho = m / M;
SinCosd(azi0, out x, out y);
x *= rho; y *= rho;
}
return(x, y);
}
