public override Vector2 <decimal> EquatorialCoordinates(DateTime date)
{
var pos = EclipticEarth3D(date);
#if DEBUG
Console.WriteLine($"Sun ecliptic position: X={pos.X} Y={pos.Y} Z={pos.Z}");
#endif
var tiltRad = CommonCalculations.GetAxialTilt(date) * DecimalMath.DegToRad;
var Xe = pos.X;
var Ye = pos.Y * DecimalMath.Cos(tiltRad);
var Ze = pos.Y * DecimalMath.Sin(tiltRad);
#if DEBUG
Console.WriteLine($"Sun equatorial position: X={Xe} Y={Ye} Z={Ze} with tilt {tiltRad}");
#endif
var RA = DecimalMath.Atan2(Ye, Xe) * DecimalMath.RadToDeg;
var Dec = DecimalMath.Atan2(Ze, DecimalMath.Sqrt(Xe * Xe + Ye * Ye)) * DecimalMath.RadToDeg;
#if DEBUG
Console.WriteLine($"Sun RA = {RA} Dec={Dec}");
#endif
return(new Vector2 <decimal>(CommonCalculations.From0To360(RA), Dec));
}
public override Vector2 <decimal> EquatorialCoordinates(DateTime date)
{
var pos = EclipticEarth3D(date);
var X = pos.X; var Y = pos.Y; var Z = pos.Z;
var R = DecimalMath.Sqrt(X * X + Y * Y + Z * Z);
var lambda = DecimalMath.Atan2(Y, X);
var sinLambda = DecimalMath.Sin(lambda);
var cosLambda = DecimalMath.Cos(lambda);
var beta = DecimalMath.Asin(Z / R);
var tanBeta = DecimalMath.Tan(beta);
var sinBeta = DecimalMath.Sin(beta);
var cosBeta = DecimalMath.Cos(beta);
var tilt = CommonCalculations.GetAxialTilt(date) * DecimalMath.DegToRad;
var cosTilt = DecimalMath.Cos(tilt);
var sinTilt = DecimalMath.Sin(tilt);
var RA = DecimalMath.Atan2(sinLambda * cosTilt - tanBeta * sinTilt, cosLambda) * DecimalMath.RadToDeg;
var Dec = DecimalMath.Asin(sinBeta * cosTilt + cosBeta * sinTilt * sinLambda) * DecimalMath.RadToDeg;
RA = CommonCalculations.From0To360(RA);
#if DEBUG
Console.WriteLine($"R = {R} lambda = {lambda}, beta = {beta}, tilt = {tilt}, RA = {RA}, dec = {Dec}");
#endif
return(new Vector2 <decimal>(RA, Dec));
}
public override Vector2 <decimal> EclipticCoordinates(DateTime date)
{
var pos = EclipticEarth3D(date);
var lon = DecimalMath.Atan2(pos.Y, pos.X) * DecimalMath.RadToDeg;
var lat = DecimalMath.Asin(pos.Z / DecimalMath.Sqrt(pos.X * pos.X + pos.Y * pos.Y + pos.Z * pos.Z)) * DecimalMath.RadToDeg;
return(new Vector2 <decimal>(CommonCalculations.From0To360(lon), lat));
}
public decimal GetValue(decimal from0To1)
{
if (from0To1 < eps)
{
return(0m);
}
return(DecimalMath.Sqrt(from0To1));
}
public void Sqrt()
{
const decimal expected = 9.0M;
decimal actual = 81.0M;
actual = DecimalMath.Sqrt(actual);
Assert.AreEqual <decimal>(expected, actual);
}
public override Vector2 <decimal> ApparentEclipticEarth(DateTime date)
{
var pos = ApparentEclipticEarth3D(date);
var lon = DecimalMath.Atan2(pos.Y, pos.X) * DecimalMath.RadToDeg;
var lat = DecimalMath.Asin(pos.Z / DecimalMath.Sqrt(pos.X * pos.X + pos.Y * pos.Y + pos.Z * pos.Z)) * DecimalMath.RadToDeg;
lon = CommonCalculations.From0To360(lon);
lat = CommonCalculations.From0To360(lat);
return(new Vector2 <decimal>(lon, lat));
}
public void TanSqrt3()
{
const decimal THREE = 3.0M;
decimal expected = DecimalMath.Sqrt(THREE);
decimal actual = DecimalMath.PI / THREE;
actual = DecimalMath.Tan(actual);
expected = Math.Round(expected, 22); //1.7320508075688772935274463415
actual = Math.Round(actual, 22); //1.7320508075688772935274463414
Assert.AreEqual <decimal>(expected, actual);
}
public Vector2 <decimal> EquatorialCoordinates(DateTime date)
{
var tilt = CommonCalculations.GetAxialTilt(date) * DecimalMath.DegToRad;
var sintilt = DecimalMath.Sin(tilt);
var costilt = DecimalMath.Cos(tilt);
var pos = EclipticEarthXYZ(date);
var xe = pos.X;
var ye = pos.Y * costilt - pos.Z * sintilt;
var ze = pos.Y * sintilt - pos.Z * costilt;
#if DEBUG
Console.WriteLine($"Pluto equatorial X= {xe}, Y = {ye}, Z = {ze}");
#endif
var RA = DecimalMath.Atan2(ye, xe) * DecimalMath.RadToDeg;
var Dec = DecimalMath.Atan2(ze, DecimalMath.Sqrt(xe * xe, ye * ye)) * DecimalMath.RadToDeg;
#if DEBUG
Console.WriteLine($"Pluto Ra= {RA}, DEC = {Dec}");
#endif
return(new Vector2 <decimal>(CommonCalculations.From0To360(RA), Dec));
}
public void SquareRoot(decimal number)
{
DecimalMath.Sqrt(number);
}
public override Vector3 <decimal> EclipticSun3D(DateTime date)
{
var degToRad = DecimalMath.Pi / 180;
var days = JulianDateCalculator.ToJulianDaysJ2000(date);
var M = MeanAnomaly(days);
var MRad = M * degToRad;
var e = Eccentricity(days);
#if DEBUG
Console.WriteLine($"Days = {days} Mean Anomaly={M} Eccentricity = {e}");
#endif
var sinM = DecimalMath.Sin(MRad);
var sin2M = DecimalMath.Sin(2 * MRad);
var sin3M = DecimalMath.Sin(3 * MRad);
var sin4M = DecimalMath.Sin(4 * MRad);
var sin5M = DecimalMath.Sin(5 * MRad);
var sin6M = DecimalMath.Sin(6 * MRad);
var e2 = DecimalMath.Power(e, 2);
var e3 = DecimalMath.Power(e, 3);
var e4 = DecimalMath.Power(e, 4);
var e5 = DecimalMath.Power(e, 5);
var e6 = DecimalMath.Power(e, 6);
var eccentricAnomalyRad =
MRad
+ e * sinM
+ e2 * 0.5m * sin2M
+ e3 * (0.375m * sin3M - 0.125m * sinM)
+ e4 * (-(1m / 6m) * sin2M + (1m / 3m) * sin4M)
+ e5 * (-(27m / 128m) * sin3M + (1m / 192m) * sinM + (125m / 384m) * sin5M)
+ e6 * ((1m / 48m) * sin2M + (27 / 80) * sin6M - (4 / 15) * sin4M);
#if DEBUG
Console.WriteLine($"Eccentric Anomaly {eccentricAnomalyRad * DecimalMath.RadToDeg}");
#endif
// Calculate true anomaly
var A = SemimajorAxis(days);
var Xv = A * (DecimalMath.Cos(eccentricAnomalyRad) - e);
var Yv = A * DecimalMath.Sqrt(1.0m - e * e) * DecimalMath.Sin(eccentricAnomalyRad);
var v = DecimalMath.Atan2(Yv, Xv);
var r = DecimalMath.Sqrt(Xv * Xv + Yv * Yv);
//Calculate Heliocentric coordinates
var N = LongAscedingNode(days) * degToRad;
var cosN = DecimalMath.Cos(N);
var sinN = DecimalMath.Sin(N);
var i = Inclination(days) * degToRad;
var cosi = DecimalMath.Cos(i);
var sini = DecimalMath.Sin(i);
var w = Peryhelion(days) * degToRad;
var cosVW = DecimalMath.Cos(v + w);
var sinVW = DecimalMath.Sin(v + w);
#if DEBUG
Console.WriteLine($"LongAscNode : {LongAscedingNode(days)}, Inclination : {Inclination(days)}");
Console.WriteLine($"Peryhelion: {Peryhelion(days)} true anomaly : {DecimalMath.Atan2(Yv, Xv) * DecimalMath.RadToDeg}");
#endif
var Xh = r * (cosN * cosVW - sinN * sinVW * cosi);
var Yh = r * (sinN * cosVW + cosN * sinVW * cosi);
var Zh = r * (sinVW * sini);
#if DEBUG
Console.WriteLine($"{Name} heliocentric coordinates {Xh} {Yh} {Zh}");
#endif
return(new Vector3 <decimal>(Xh, Yh, Zh));
}
public decimal calculate(Queue <string> polska, decimal x)
{
decimal answer = 0;
Stack <decimal> opers = new Stack <decimal>();
foreach (string s in polska)
{
if (standartOperators.Contains(s))
{
decimal a;
decimal b;
switch (s)
{
case "+":
opers.Push(opers.Pop() + opers.Pop());
break;
case "-":
b = opers.Pop();
a = opers.Pop();
opers.Push(a - b);
break;
case "*":
opers.Push(opers.Pop() * opers.Pop());
break;
case "/":
b = opers.Pop();
a = opers.Pop();
opers.Push(a / b);
break;
case "^":
b = opers.Pop();
a = opers.Pop();
opers.Push(DecimalMath.Pow(a, b));
break;
case "%":
b = opers.Pop();
a = opers.Pop();
opers.Push(a % b);
break;
case "sqrt":
opers.Push(DecimalMath.Sqrt(opers.Pop()));
break;
case "sin":
opers.Push(DecimalMath.Sin(opers.Pop()));
break;
case "cos":
opers.Push(DecimalMath.Cos(opers.Pop()));
break;
case "tan":
opers.Push(DecimalMath.Tan(opers.Pop()));
break;
case "atan":
opers.Push(DecimalMath.Atan(opers.Pop()));
break;
case "acos":
opers.Push(DecimalMath.Acos(opers.Pop()));
break;
case "asin":
opers.Push(DecimalMath.Asin(opers.Pop()));
break;
case "acotan":
opers.Push(DecimalMath.Atan(1 / opers.Pop()));
break;
case "exp":
opers.Push(DecimalMath.Exp(opers.Pop()));
break;
case "log":
opers.Push(DecimalMath.Log(opers.Pop()));
break;
case "ln":
opers.Push(DecimalMath.Log10(opers.Pop()));
break;
case "sinh":
opers.Push(DecimalMath.Sinh(opers.Pop()));
break;
case "cosh":
opers.Push(DecimalMath.Cosh(opers.Pop()));
break;
case "tanh":
opers.Push(DecimalMath.Tanh(opers.Pop()));
break;
case "abs":
opers.Push(DecimalMath.Abs(opers.Pop()));
break;
case "ceil":
opers.Push(DecimalMath.Ceiling(opers.Pop()));
break;
case "floor":
opers.Push(DecimalMath.Floor(opers.Pop()));
break;
case "fac":
opers.Push(factorial(opers.Pop()));
break;
case "sfac":
opers.Push(semifactorial(opers.Pop()));
break;
case "round":
opers.Push(DecimalMath.Round(opers.Pop()));
break;
case "fpart":
a = opers.Pop();
opers.Push(a - DecimalMath.Truncate(a));
break;
}
}
else if (s == "x")
{
opers.Push(x);
}
else
{
opers.Push(decimal.Parse(s));
}
}
answer = opers.Pop();
return(answer);
}
/// <summary>
/// Returns distances between two decimal Vector2 instances
/// </summary>
/// <param name="V1"></param>
/// <param name="V2"></param>
/// <returns></returns>
public static decimal Distance(Vector2 <decimal> V1, Vector2 <decimal> V2)
{
return(DecimalMath.Sqrt(DecimalMath.Power(V1.X - V2.X, 2) + DecimalMath.Power(V1.Y - V2.Y, 2)));
}
/// <summary>
/// Calculate Euclidean metric for 3D points
/// </summary>
/// <param name="v1"></param>
/// <param name="v2"></param>
/// <returns></returns>
public static decimal Distance(Vector3 <decimal> v1, Vector3 <decimal> v2)
{
return(DecimalMath.Sqrt(DecimalMath.Power(v1.X - v2.X, 2) + DecimalMath.Power(v1.Y - v2.Y, 2) + DecimalMath.Power(v1.Z - v2.Z, 2)));
}