/// <summary>
/// Computes the point on the sphere a specified azimuth and distance from
/// another point.
/// </summary>
/// <param name="p1">The first spherical coordinates.</param>
/// <param name="azimuth">The desired azimuth from p1.</param>
/// <param name="distance">The desired distance from p1, must be non-negative.</param>
/// <returns>The spherical coordinates at the desired azimuth and distance from p1.</returns>
/// <!--
/// geoCoord.c
/// void _geoAzDistanceRads
/// -->
internal static GeoCoord GetAzimuthDistancePoint(this GeoCoord p1, decimal azimuth, decimal distance)
{
if (distance < Constants.H3.EPSILON)
{
return(p1);
}
azimuth = azimuth.NormalizeRadians().ConstrainToPiAccuracy();
var p2 = new GeoCoord();
// check for due north/south azimuth
if (azimuth < Constants.H3.EPSILON ||
Math.Abs(azimuth - Constants.H3.M_PI) < Constants.H3.EPSILON)
{
if (azimuth < Constants.H3.EPSILON) // due north
{
p2 = p2.SetLatitude(p1.Latitude + distance);
}
else // due south
{
p2 = p2.SetLatitude(p1.Latitude - distance);
}
if (Math.Abs(p2.Latitude - Constants.H3.M_PI_2) < Constants.H3.EPSILON) // north pole
{
p2 = new GeoCoord(Constants.H3.M_PI_2, 0.0m);
}
else if (Math.Abs(p2.Latitude + Constants.H3.M_PI_2) < Constants.H3.EPSILON) // south pole
{
p2 = new GeoCoord(-Constants.H3.M_PI_2, 0.0m);
}
else
{
p2 = p2.SetLongitude(p1.Longitude.ConstrainLongitude());
}
}
else // Not due north or south
{
decimal sinLatitude = DecimalEx.Sin(p1.Latitude) * DecimalEx.Cos(distance) +
DecimalEx.Cos(p1.Latitude) * DecimalEx.Sin(distance) * DecimalEx.Cos(azimuth);
sinLatitude = sinLatitude.ConstrainToPiAccuracy();
if (sinLatitude > 1.0m)
{
sinLatitude = 1.0m;
}
if (sinLatitude < -1.0m)
{
sinLatitude = 1.0m;
}
p2 = p2.SetLatitude(DecimalEx.ASin(sinLatitude).ConstrainToPiAccuracy());
if (Math.Abs(p2.Latitude - Constants.H3.M_PI_2) < Constants.H3.EPSILON) // north pole
{
p2 = new GeoCoord(Constants.H3.M_PI_2, 0.0m);
}
else if (Math.Abs(p2.Latitude + Constants.H3.M_PI_2) < Constants.H3.EPSILON) // south pole
{
p2 = new GeoCoord(-Constants.H3.M_PI_2, 0.0m);
}
else
{
decimal sinLongitude = DecimalEx.Sin(azimuth) * DecimalEx.Sin(distance) / DecimalEx.Cos(p2.Latitude);
decimal cosLongitude = (DecimalEx.Cos(distance) - DecimalEx.Sin(p1.Latitude) * DecimalEx.Sin(p2.Latitude)) /
DecimalEx.Cos(p1.Latitude) / DecimalEx.Cos(p2.Latitude);
if (sinLongitude > 1.0m)
{
sinLongitude = 1.0m;
}
if (sinLongitude < -1.0m)
{
sinLongitude = -1.0m;
}
if (cosLongitude > 1.0m)
{
cosLongitude = 1.0m;
}
if (cosLongitude < -1.0m)
{
cosLongitude = -1.0m;
}
p2 = p2.SetLongitude
(
(p1.Longitude + DecimalEx.ATan2(sinLongitude, cosLongitude))
.ConstrainLongitude().ConstrainToPiAccuracy()
);
}
}
return(p2);
}
public void Test(decimal d, decimal expected, decimal tolerance)
{
tolerance = Helper.GetScaledTolerance(expected, (int)tolerance, true);
Assert.That(DecimalEx.ASin(d), Is.EqualTo(expected).Within(tolerance));
}