/// <summary>
/// Calculates an intermediate point at any fraction along the great circle path
/// between two points with horizontal coordinates
/// </summary>
/// <param name="p1">Horizontal coordinates of the first point</param>
/// <param name="p2">Horizontal coordinates of the second point</param>
/// <param name="fraction">Fraction along great circle route (f=0 is point 1, f=1 is point 2).</param>
/// <returns>
/// The intermediate point at specified fraction
/// </returns>
/// <remarks>
/// Formula is taken from <see href="http://www.movable-type.co.uk/scripts/latlong.html"/>
/// that is originally based on <see cref="http://www.edwilliams.org/avform.htm#Intermediate"/>.
/// </remarks>
public static CrdsHorizontal Intermediate(CrdsHorizontal p1, CrdsHorizontal p2, double fraction)
{
if (fraction < 0 || fraction > 1)
{
throw new ArgumentException("Fraction value should be in range [0, 1]", nameof(fraction));
}
double d = ToRadians(Separation(p1, p2));
double a, b;
if (d <= 1e-6)
{
a = 1 - fraction;
b = fraction;
}
else
{
a = Math.Sin((1 - fraction) * d) / Math.Sin(d);
b = Math.Sin(fraction * d) / Math.Sin(d);
}
double alt1 = ToRadians(p1.Altitude);
double alt2 = ToRadians(p2.Altitude);
double az1 = ToRadians(p1.Azimuth);
double az2 = ToRadians(p2.Azimuth);
double x = a * Math.Cos(alt1) * Math.Cos(az1) + b * Math.Cos(alt2) * Math.Cos(az2);
double y = a * Math.Cos(alt1) * Math.Sin(az1) + b * Math.Cos(alt2) * Math.Sin(az2);
double z = a * Math.Sin(alt1) + b * Math.Sin(alt2);
double alt = Math.Atan2(z, Math.Sqrt(x * x + y * y));
double az = Math.Atan2(y, x);
return(new CrdsHorizontal(ToDegrees(az), ToDegrees(alt)));
}
public static CrdsHorizontal WithRefraction(this CrdsHorizontal h0)
{
//if (h0.Altitude < 0) return h0;
double R = 1.02 / Math.Tan(Angle.ToRadians(h0.Altitude + 10.3 / (h0.Altitude + 5.11)));
return(new CrdsHorizontal(h0.Azimuth, h0.Altitude + R / 60));
}
/// <summary>
/// Calculates angular separation between two points with horizontal coordinates
/// </summary>
/// <param name="p1">Horizontal coordinates of the first point</param>
/// <param name="p2">Horizontal coordinates of the second point</param>
/// <returns>Angular separation in degrees</returns>
public static double Separation(CrdsHorizontal p1, CrdsHorizontal p2)
{
double a1 = ToRadians(p1.Altitude);
double a2 = ToRadians(p2.Altitude);
double A1 = p1.Azimuth;
double A2 = p2.Azimuth;
double a = Math.Acos(
Math.Sin(a1) * Math.Sin(a2) +
Math.Cos(a1) * Math.Cos(a2) * Math.Cos(ToRadians(A1 - A2)));
return(double.IsNaN(a) ? 0 : ToDegrees(a));
}
/// <summary>
/// Converts local horizontal coordinates to equatorial coordinates.
/// </summary>
/// <param name="hor">Pair of local horizontal coordinates.</param>
/// <param name="geo">Geographical of the observer</param>
/// <param name="theta0">Local sidereal time.</param>
/// <returns>Pair of equatorial coordinates</returns>
public static CrdsEquatorial ToEquatorial(this CrdsHorizontal hor, CrdsGeographical geo, double theta0)
{
CrdsEquatorial eq = new CrdsEquatorial();
double A = Angle.ToRadians(hor.Azimuth);
double h = Angle.ToRadians(hor.Altitude);
double phi = Angle.ToRadians(geo.Latitude);
double Y = Math.Sin(A);
double X = Math.Cos(A) * Math.Sin(phi) + Math.Tan(h) * Math.Cos(phi);
double H = Angle.ToDegrees(Math.Atan2(Y, X));
eq.Alpha = Angle.To360(theta0 - geo.Longitude - H);
eq.Delta = Angle.ToDegrees(Math.Asin(Math.Sin(phi) * Math.Sin(h) - Math.Cos(phi) * Math.Cos(h) * Math.Cos(A)));
return(eq);
}
/// <summary>
/// Converts equatorial coodinates to local horizontal
/// </summary>
/// <param name="eq">Pair of equatorial coodinates</param>
/// <param name="geo">Geographical coordinates of the observer</param>
/// <param name="theta0">Local sidereal time</param>
/// <remarks>
/// Implementation is taken from AA(I), formulae 12.5, 12.6.
/// </remarks>
public static CrdsHorizontal ToHorizontal(this CrdsEquatorial eq, CrdsGeographical geo, double theta0)
{
double H = Angle.ToRadians(HourAngle(theta0, geo.Longitude, eq.Alpha));
double phi = Angle.ToRadians(geo.Latitude);
double delta = Angle.ToRadians(eq.Delta);
CrdsHorizontal hor = new CrdsHorizontal();
double Y = Math.Sin(H);
double X = Math.Cos(H) * Math.Sin(phi) - Math.Tan(delta) * Math.Cos(phi);
hor.Altitude = Angle.ToDegrees(Math.Asin(Math.Sin(phi) * Math.Sin(delta) + Math.Cos(phi) * Math.Cos(delta) * Math.Cos(H)));
hor.Azimuth = Angle.ToDegrees(Math.Atan2(Y, X));
hor.Azimuth = Angle.To360(hor.Azimuth);
return(hor);
}
/// <summary>
/// Sets horizontal coordinates values.
/// </summary>
/// <param name="other">Instance of coordinates to be copied.</param>
public void Set(CrdsHorizontal other)
{
Azimuth = other.Azimuth;
Altitude = other.Altitude;
}
/// <summary>
/// Creates a pair of horizontal coordinates by copying from other instance.
/// </summary>
/// <param name="other">Instance of coordinates to be copied.</param>
public CrdsHorizontal(CrdsHorizontal other)
{
Azimuth = other.Azimuth;
Altitude = other.Altitude;
}