/// <summary>
/// Set the central point of the projection
/// </summary>
/// <param name="lat0">latitude of center point of projection (degrees).</param>
/// <param name="lon0">longitude of center point of projection (degrees).</param>
/// <remarks>
/// <paramref name="lat0"/> should be in the range [−90°, 90°].
/// </remarks>
public void Reset(double lat0, double lon0)
{
_meridian = _earth.Line(lat0, lon0, 0,
GeodesicFlags.Latitude | GeodesicFlags.Longitude |
GeodesicFlags.Distance | GeodesicFlags.DistanceIn |
GeodesicFlags.Azimuth);
var f = _earth.Flattening;
SinCosd(LatitudeOrigin, out _sbet0, out _cbet0);
_sbet0 *= (1 - f);
Norm(ref _sbet0, ref _cbet0);
}
/// <summary>
/// Reverse projection, from gnomonic to geographic.
/// </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="x">easting of point (meters).</param>
/// <param name="y">northing of point (meters).</param>
/// <param name="azi">azimuth of geodesic at point (degrees).</param>
/// <param name="rk">reciprocal of azimuthal scale at point.</param>
/// <returns>
/// <i>lat</i>, latitude of point (degrees) and <i>lon</i>, longitude of point (degrees).
/// </returns>
/// <remarks>
/// <paramref name="lat0"/> should be in the range [−90°, 90°].
/// <i>lat</i> will be in the range [−90°, 90°] and <i>lon</i> will be in the range [−180°, 180°].
/// 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. Even though all inputs should return a valid <i>lat</i> and <i>lon</i>,
/// it's possible that the procedure fails to converge for very large <paramref name="x"/> or <paramref name="y"/>;
/// in this case <see cref="double.NaN"/>s are returned for all the output arguments.
/// A call to <see cref="Reverse(double, double, double, double, out double, out double)"/> followed by a call to
/// <see cref="Forward(double, double, double, double, out double, out double)"/>
/// will return the original (<paramref name="x"/>, <paramref name="y"/>) (to roundoff).
/// </remarks>
public (double lat, double lon) Reverse(double lat0, double lon0, double x, double y, out double azi, out double rk)
{
double
lat, lon,
azi0 = Atan2d(x, y),
rho = Hypot(x, y),
s = _a * Atan(rho / _a);
bool little = rho <= _a;
if (!little)
{
rho = 1 / rho;
}
var line = _earth.Line(lat0, lon0, azi0,
GeodesicFlags.Latitude | GeodesicFlags.Longitude |
GeodesicFlags.Azimuth | GeodesicFlags.DistanceIn |
GeodesicFlags.ReducedLength | GeodesicFlags.GeodesicScale);
int count = numit_, trip = 0;
double lat1 = 0, lon1 = 0, azi1 = 0, M = 0;
while (count-- != 0 || GEOGRAPHICLIB_PANIC)
{
line.Position(s, out lat1, out lon1, out azi1, out var m, out M, out _);
if (trip != 0)
{
break;
}
// If little, solve rho(s) = rho with drho(s)/ds = 1/M^2
// else solve 1/rho(s) = 1/rho with d(1/rho(s))/ds = -1/m^2
var ds = little ? (m - rho * M) * M : (rho * m - M) * m;
s -= ds;
// Reversed test to allow escape with NaNs
if (!(Abs(ds) >= eps_ * _a))
{
++trip;
}
}
if (trip != 0)
{
(lat, lon, azi, rk) = (lat1, lon1, azi1, M);
}
else
{
lat = lon = azi = rk = double.NaN;
}
return(lat, lon);
}