/**
* Forward projection, from geographic to gnomonic.
* <p>
* @param lat0 latitude of center point of projection (degrees).
* @param lon0 longitude of center point of projection (degrees).
* @param lat latitude of point (degrees).
* @param lon longitude of point (degrees).
* @return {@link GnomonicData} object with the following fields:
* <i>lat0</i>, <i>lon0</i>, <i>lat</i>, <i>lon</i>, <i>x</i>, <i>y</i>,
* <i>azi</i>, <i>rk</i>.
* <p>
* <i>lat0</i> and <i>lat</i> should be in the range [−90°,
* 90°] and <i>lon0</i> and <i>lon</i> should be in the range
* [−540°, 540°). The scale of the projection is
* 1/<i>rk<sup>2</sup></i> in the "radial" direction, <i>azi</i> clockwise
* from true north, and is 1/<i>rk</i> in the direction perpendicular to
* this. If the point lies "over the horizon", i.e., if <i>rk</i> ≤ 0,
* then NaNs are returned for <i>x</i> and <i>y</i> (the correct values are
* returned for <i>azi</i> and <i>rk</i>). A call to Forward followed by a
* call to Reverse will return the original (<i>lat</i>, <i>lon</i>) (to
* within roundoff) provided the point in not over the horizon.
*/
public GnomonicData Forward(double lat0, double lon0, double lat, double lon)
{
GeodesicData inv =
_earth.Inverse(lat0, lon0, lat, lon,
GeodesicMask.AZIMUTH | GeodesicMask.GEODESICSCALE |
GeodesicMask.REDUCEDLENGTH);
GnomonicData fwd =
new GnomonicData(lat0, lon0, lat, lon, Double.NaN, Double.NaN,
inv.FinalAzimuth, inv.GeodesicScale12);
if (inv.GeodesicScale12 > 0)
{
double rho = inv.ReducedLength / inv.GeodesicScale12;
Pair p = GeoMath.SinCosD(inv.InitialAzimuth);
fwd.x = rho * p.First;
fwd.y = rho * p.Second;
}
return(fwd);
}
/**
* Reverse projection, from gnomonic to geographic.
* <p>
* @param lat0 latitude of center point of projection (degrees).
* @param lon0 longitude of center point of projection (degrees).
* @param x easting of point (meters).
* @param y northing of point (meters).
* @return {@link GnomonicData} object with the following fields:
* <i>lat0</i>, <i>lon0</i>, <i>lat</i>, <i>lon</i>, <i>x</i>, <i>y</i>,
* <i>azi</i>, <i>rk</i>.
* <p>
* <i>lat0</i> should be in the range [−90°, 90°] and
* <i>lon0</i> should be in the range [−540°, 540°).
* <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/<i>rk<sup>2</sup></i> in the "radial" direction,
* <i>azi</i> clockwise from true north, and is 1/<i>rk</i> 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 <i>x</i> or <i>y</i>; in this case NaNs are
* returned for all the output arguments. A call to Reverse followed by a
* call to Forward will return the original (<i>x</i>, <i>y</i>) (to
* roundoff).
*/
public GnomonicData Reverse(double lat0, double lon0, double x, double y)
{
GnomonicData rev =
new GnomonicData(lat0, lon0, Double.NaN, Double.NaN, x, y, Double.NaN,
Double.NaN);
double azi0 = GeoMath.Atan2d(x, y);
double rho = GeoMath.Hypot(x, y);
double s = _a * Math.Atan(rho / _a);
bool little = rho <= _a;
if (!little)
{
rho = 1 / rho;
}
GeodesicLine line =
_earth.Line(lat0, lon0, azi0, GeodesicMask.LATITUDE
| GeodesicMask.LONGITUDE | GeodesicMask.AZIMUTH
| GeodesicMask.DISTANCE_IN | GeodesicMask.REDUCEDLENGTH
| GeodesicMask.GEODESICSCALE);
int count = numit_, trip = 0;
GeodesicData pos = null;
while (count-- > 0)
{
pos =
line.Position(s, GeodesicMask.LONGITUDE | GeodesicMask.LATITUDE
| GeodesicMask.AZIMUTH | GeodesicMask.DISTANCE_IN
| GeodesicMask.REDUCEDLENGTH
| GeodesicMask.GEODESICSCALE);
if (trip > 0)
{
break;
}
double ds =
little ? ((pos.ReducedLength / pos.GeodesicScale12) - rho) * pos.GeodesicScale12 * pos.GeodesicScale12
: (rho - (pos.GeodesicScale12 / pos.ReducedLength)) * pos.ReducedLength * pos.ReducedLength;
s -= ds;
if (Math.Abs(ds) <= eps_ * _a)
{
trip++;
}
}
if (trip == 0)
{
return(rev);
}
rev.PointLatitude = pos.Latitude2;
rev.PointLongitude = pos.Longitude2;
rev.azi = pos.FinalAzimuth;
rev.rk = pos.GeodesicScale12;
return(rev);
}
