/// <summary>
/// Gets the descending node of orbit.
/// </summary>
/// <param name="desc">The desc.</param>
/// <returns><c>true</c> if descending node exists, otherwise <c>false</c></returns>
public bool GetDescendingNode(out Vector3d desc)
{
var norm = CelestialBodyUtils.CrossProduct(OrbitNormal, EclipticNormal);
var s = CelestialBodyUtils.DotProduct(CelestialBodyUtils.CrossProduct(norm, SemiMajorAxisBasis), OrbitNormal) < 0;
var ecc = 0d;
var trueAnom = Vector3d.Angle(norm, -CenterPoint) * Mathd.Deg2Rad;
if (Eccentricity < 1)
{
var cosT = Math.Cos(trueAnom);
ecc = Math.Acos((Eccentricity + cosT) / (1d + Eccentricity * cosT));
if (s)
{
ecc = Mathd.PI_2 - ecc;
}
}
else
{
trueAnom = Vector3d.Angle(norm, CenterPoint) * Mathd.Deg2Rad;
if (trueAnom >= Mathd.Acos(-1d / Eccentricity))
{
desc = new Vector3d();
return(false);
}
var cosT = Math.Cos(trueAnom);
ecc = CelestialBodyUtils.Acosh((Eccentricity + cosT) / (1 + Eccentricity * cosT)) * (s ? -1 : 1);
}
desc = GetFocalPositionAtEccentricAnomaly(ecc);
return(true);
}
public bool GetAscendingNode(out Vector3d asc)
{
var norm = CelestialBodyUtils.CrossProduct(orbitNormal, eclipticNormal);
var s = CelestialBodyUtils.DotProduct(CelestialBodyUtils.CrossProduct(norm, semiMajorAxisBasis), orbitNormal) < 0;
var ecc = 0d;
var trueAnom = Vector3d.Angle(norm, centerPoint) * Mathd.Deg2Rad;
if (eccentricity < 1)
{
var cosT = System.Math.Cos(trueAnom);
ecc = System.Math.Acos((eccentricity + cosT) / (1d + eccentricity * cosT));
if (!s)
{
ecc = Mathd.PI_2 - ecc;
}
}
else
{
trueAnom = Vector3d.Angle(-norm, centerPoint) * Mathd.Deg2Rad;
if (trueAnom >= Mathd.Acos(-1d / eccentricity))
{
asc = new Vector3d();
return(false);
}
var cosT = System.Math.Cos(trueAnom);
ecc = CelestialBodyUtils.Acosh((eccentricity + cosT) / (1 + eccentricity * cosT)) * (!s ? -1 : 1);
}
asc = GetFocalPositionAtEccentricAnomaly(ecc);
return(true);
}
/// <summary>
/// Draw two crossing lines in scene view.
/// </summary>
private static void DrawX(Vector3 pos, float size, Color col, Vector3 normal, Vector3 up)
{
Handles.color = col;
Vector3 right = CelestialBodyUtils.CrossProduct(up, normal).normalized;
Handles.DrawLine(pos + up * size, pos - up * size);
Handles.DrawLine(pos + right * size, pos - right * size);
}
public static Vector3[] CalcOrbitPoints(Vector3 attractorPos, Vector3 bodyPos, double attractorMass, double bodyMass, Vector3 relVelocity, double gConst, int pointsCount)
{
if (pointsCount < 3 || pointsCount > 10000)
{
return(new Vector3[0]);
}
var focusPoint = CalcCenterOfMass(attractorPos, attractorMass, bodyPos, bodyMass);
var radiusVector = bodyPos - focusPoint;
var radiusVectorMagnitude = radiusVector.magnitude;
var orbitNormal = CelestialBodyUtils.CrossProduct(radiusVector, relVelocity);
var MG = (attractorMass + bodyMass) * gConst;
var eccVector = CelestialBodyUtils.CrossProduct(relVelocity, orbitNormal) / (float)MG - radiusVector / radiusVectorMagnitude;
var focalParameter = orbitNormal.sqrMagnitude / MG;
var eccentricity = eccVector.magnitude;
var minorAxisNormal = -CelestialBodyUtils.CrossProduct(orbitNormal, eccVector).normalized;
var majorAxisNormal = -CelestialBodyUtils.CrossProduct(orbitNormal, minorAxisNormal).normalized;
orbitNormal.Normalize();
double orbitCompressionRatio;
double semiMajorAxys;
double semiMinorAxys;
Vector3 relFocusPoint;
Vector3 centerPoint;
if (eccentricity < 1)
{
orbitCompressionRatio = 1 - eccentricity * eccentricity;
semiMajorAxys = focalParameter / orbitCompressionRatio;
semiMinorAxys = semiMajorAxys * System.Math.Sqrt(orbitCompressionRatio);
relFocusPoint = (float)semiMajorAxys * eccVector;
centerPoint = focusPoint - relFocusPoint;
}
else
{
orbitCompressionRatio = eccentricity * eccentricity - 1f;
semiMajorAxys = focalParameter / orbitCompressionRatio;
semiMinorAxys = semiMajorAxys * System.Math.Sqrt(orbitCompressionRatio);
relFocusPoint = -(float)semiMajorAxys * eccVector;
centerPoint = focusPoint - relFocusPoint;
}
var points = new Vector3[pointsCount];
double eccVar = 0f;
for (int i = 0; i < pointsCount; i++)
{
Vector3 result = eccentricity < 1 ?
new Vector3((float)(System.Math.Sin(eccVar) * semiMinorAxys), -(float)(System.Math.Cos(eccVar) * semiMajorAxys)) :
new Vector3((float)(System.Math.Sinh(eccVar) * semiMinorAxys), (float)(System.Math.Cosh(eccVar) * semiMajorAxys));
eccVar += Mathf.PI * 2f / (float)(pointsCount - 1);
points[i] = minorAxisNormal * result.x + majorAxisNormal * result.y + centerPoint;
}
return(points);
}
private void DrawInclinationMarkForBody(CelestialBody body, float scale)
{
var norm = CelestialBodyUtils.CrossProduct((Vector3)body.OrbitData.OrbitNormal, (Vector3)_simControl.EclipticNormal);
Handles.color = Color.white;
var p = CelestialBodyUtils.CrossProduct(norm, (Vector3)_simControl.EclipticNormal).normalized;
Handles.DrawLine((Vector3)body.OrbitFocusPoint, (Vector3)body.OrbitFocusPoint + p * 3f * scale);
Handles.DrawLine((Vector3)body.OrbitFocusPoint, (Vector3)body.OrbitFocusPoint + CelestialBodyUtils.RotateVectorByAngle(p, (float)body.OrbitData.Inclination, -norm.normalized) * 3f * scale);
Handles.DrawWireArc((Vector3)body.OrbitFocusPoint, -norm, p, (float)(body.OrbitData.Inclination * Mathd.Rad2Deg), 1f * scale);
DrawLabelScaled((Vector3)body.OrbitFocusPoint + p * scale, (body.OrbitData.Inclination * Mathd.Rad2Deg).ToString("0") + "\u00B0", Color.white, 10);
}
/// <summary>
/// Draw simple arrow in scene window at given world coordinates
/// </summary>
private static void DrawArrow(Vector3 from, Vector3 to, Color col, Vector3 normal)
{
var dir = to - from;
float dist = dir.magnitude;
var dirNorm = dir / dist; //normalized vector
float headSize = dist / 6f;
var _colBefore = Handles.color;
Handles.color = col;
Vector3 sideNormal = CelestialBodyUtils.CrossProduct(dir, normal).normalized;
Handles.DrawLine(from, from + dirNorm * (dist - headSize));
Handles.DrawLine(from + dirNorm * (dist - headSize) + sideNormal * headSize / 2f, from + dirNorm * (dist - headSize) - sideNormal * headSize / 2f);
Handles.DrawLine(from + dirNorm * (dist - headSize) + sideNormal * headSize / 2f, from + dir);
Handles.DrawLine(from + dirNorm * (dist - headSize) - sideNormal * headSize / 2f, from + dir);
Handles.color = _colBefore;
}
/// <summary>
/// Calculates the full state of orbit from current body position, attractor position, attractor mass, velocity, and gravConstant.
/// </summary>
public void CalculateNewOrbitData()
{
IsDirty = false;
var MG = AttractorMass * GravitationalConstant;
AttractorDistance = Position.magnitude;
var angularMomentumVector = CelestialBodyUtils.CrossProduct(Position, Velocity);
OrbitNormal = angularMomentumVector.normalized;
Vector3d eccVector;
// Check if zero lenght.
if (OrbitNormal.sqrMagnitude < 0.9 || OrbitNormal.sqrMagnitude > 1.1)
{
OrbitNormal = CelestialBodyUtils.CrossProduct(Position, EclipticUp).normalized;
eccVector = new Vector3d();
}
else
{
eccVector = CelestialBodyUtils.CrossProduct(Velocity, angularMomentumVector) / MG - Position / AttractorDistance;
}
OrbitNormalDotEclipticNormal = CelestialBodyUtils.DotProduct(OrbitNormal, EclipticNormal);
FocalParameter = angularMomentumVector.sqrMagnitude / MG;
Eccentricity = eccVector.magnitude;
EnergyTotal = Velocity.sqrMagnitude - 2 * MG / AttractorDistance;
SemiMinorAxisBasis = CelestialBodyUtils.CrossProduct(angularMomentumVector, eccVector).normalized;
if (SemiMinorAxisBasis.sqrMagnitude < 0.5)
{
SemiMinorAxisBasis = CelestialBodyUtils.CrossProduct(OrbitNormal, Position).normalized;
}
SemiMajorAxisBasis = CelestialBodyUtils.CrossProduct(OrbitNormal, SemiMinorAxisBasis).normalized;
Inclination = Vector3d.Angle(OrbitNormal, EclipticNormal) * Mathd.Deg2Rad;
if (Eccentricity < 1)
{
OrbitCompressionRatio = 1 - Eccentricity * Eccentricity;
SemiMajorAxis = FocalParameter / OrbitCompressionRatio;
SemiMinorAxis = SemiMajorAxis * Math.Sqrt(OrbitCompressionRatio);
CenterPoint = -SemiMajorAxis * eccVector;
Period = Mathd.PI_2 * Mathd.Sqrt(Mathd.Pow(SemiMajorAxis, 3) / MG);
Apoapsis = CenterPoint + SemiMajorAxisBasis * SemiMajorAxis;
Periapsis = CenterPoint - SemiMajorAxisBasis * SemiMajorAxis;
PeriapsisDistance = Periapsis.magnitude;
ApoapsisDistance = Apoapsis.magnitude;
TrueAnomaly = Vector3d.Angle(Position, -SemiMajorAxisBasis) * Mathd.Deg2Rad;
if (CelestialBodyUtils.DotProduct(CelestialBodyUtils.CrossProduct(Position, SemiMajorAxisBasis), OrbitNormal) < 0)
{
TrueAnomaly = Mathd.PI_2 - TrueAnomaly;
}
EccentricAnomaly = CelestialBodyUtils.ConvertTrueToEccentricAnomaly(TrueAnomaly, Eccentricity);
MeanAnomaly = EccentricAnomaly - Eccentricity * Math.Sin(EccentricAnomaly);
}
else
{
OrbitCompressionRatio = Eccentricity * Eccentricity - 1;
SemiMajorAxis = FocalParameter / OrbitCompressionRatio;
SemiMinorAxis = SemiMajorAxis * Math.Sqrt(OrbitCompressionRatio);
CenterPoint = SemiMajorAxis * eccVector;
Period = double.PositiveInfinity;
Apoapsis = new Vector3d(double.PositiveInfinity, double.PositiveInfinity, double.PositiveInfinity);
Periapsis = CenterPoint + SemiMajorAxisBasis * (SemiMajorAxis);
PeriapsisDistance = Periapsis.magnitude;
ApoapsisDistance = double.PositiveInfinity;
TrueAnomaly = Vector3d.Angle(Position, eccVector) * Mathd.Deg2Rad;
if (CelestialBodyUtils.DotProduct(CelestialBodyUtils.CrossProduct(Position, SemiMajorAxisBasis), OrbitNormal) < 0)
{
TrueAnomaly = -TrueAnomaly;
}
EccentricAnomaly = CelestialBodyUtils.ConvertTrueToEccentricAnomaly(TrueAnomaly, Eccentricity);
MeanAnomaly = Math.Sinh(EccentricAnomaly) * Eccentricity - EccentricAnomaly;
}
}
public void CalculateNewOrbitData()
{
isDirty = false;
var MG = attractorMass * gravConst;
attractorDistance = position.magnitude;
var angularMomentumVector = CelestialBodyUtils.CrossProduct(position, velocity);
orbitNormal = angularMomentumVector.normalized;
Vector3d eccVector;
if (orbitNormal.sqrMagnitude < 0.9 || orbitNormal.sqrMagnitude > 1.1) //check if zero lenght
{
orbitNormal = CelestialBodyUtils.CrossProduct(position, eclipticUp).normalized;
eccVector = new Vector3d();
}
else
{
eccVector = CelestialBodyUtils.CrossProduct(velocity, angularMomentumVector) / MG - position / attractorDistance;
}
orbitNormalDotEclipticNormal = CelestialBodyUtils.DotProduct(orbitNormal, eclipticNormal);
focalParameter = angularMomentumVector.sqrMagnitude / MG;
eccentricity = eccVector.magnitude;
//if (debug) {
// string format = "0.0000000000";
// Debug.Log(
// "ECC: " + eccVector.ToString(format) + " LEN: " + eccVector.magnitude.ToString(format) + "\n" +
// "POS: " + position.ToString(format) + " LEN: " + position.magnitude.ToString(format) + "\n" +
// "POSNORM: " + ( position / attractorDistance ).ToString(format) + " LEN: " + ( position / attractorDistance ).magnitude.ToString(format) + "\n" +
// "VEL: " + velocity.ToString(format) + " LEN: " + velocity.magnitude.ToString(format) + "\n" +
// "POScrossVEL: " + angularMomentumVector.ToString(format) + " LEN: " + angularMomentumVector.magnitude.ToString(format) + "\n"
// );
//}
energyTotal = velocity.sqrMagnitude - 2 * MG / attractorDistance;
semiMinorAxisBasis = CelestialBodyUtils.CrossProduct(angularMomentumVector, eccVector).normalized;
if (semiMinorAxisBasis.sqrMagnitude < 0.5)
{
semiMinorAxisBasis = CelestialBodyUtils.CrossProduct(orbitNormal, position).normalized;
}
semiMajorAxisBasis = CelestialBodyUtils.CrossProduct(orbitNormal, semiMinorAxisBasis).normalized;
inclination = Vector3d.Angle(orbitNormal, eclipticNormal) * Mathd.Deg2Rad;
if (eccentricity < 1)
{
orbitCompressionRatio = 1 - eccentricity * eccentricity;
semiMajorAxis = focalParameter / orbitCompressionRatio;
semiMinorAxis = semiMajorAxis * System.Math.Sqrt(orbitCompressionRatio);
centerPoint = -semiMajorAxis * eccVector;
period = Mathd.PI_2 * Mathd.Sqrt(Mathd.Pow(semiMajorAxis, 3) / MG);
apoapsis = centerPoint + semiMajorAxisBasis * semiMajorAxis;
periapsis = centerPoint - semiMajorAxisBasis * semiMajorAxis;
periapsisDistance = periapsis.magnitude;
apoapsisDistance = apoapsis.magnitude;
trueAnomaly = Vector3d.Angle(position, -semiMajorAxisBasis) * Mathd.Deg2Rad;
if (CelestialBodyUtils.DotProduct(CelestialBodyUtils.CrossProduct(position, semiMajorAxisBasis), orbitNormal) < 0)
{
trueAnomaly = Mathd.PI_2 - trueAnomaly;
}
eccentricAnomaly = CelestialBodyUtils.ConvertTrueToEccentricAnomaly(trueAnomaly, eccentricity);
meanAnomaly = eccentricAnomaly - eccentricity * System.Math.Sin(eccentricAnomaly);
}
else
{
orbitCompressionRatio = eccentricity * eccentricity - 1;
semiMajorAxis = focalParameter / orbitCompressionRatio;
semiMinorAxis = semiMajorAxis * System.Math.Sqrt(orbitCompressionRatio);
centerPoint = semiMajorAxis * eccVector;
period = double.PositiveInfinity;
apoapsis = new Vector3d(double.PositiveInfinity, double.PositiveInfinity, double.PositiveInfinity);
periapsis = centerPoint + semiMajorAxisBasis * (semiMajorAxis);
periapsisDistance = periapsis.magnitude;
apoapsisDistance = double.PositiveInfinity;
trueAnomaly = Vector3d.Angle(position, eccVector) * Mathd.Deg2Rad;
if (CelestialBodyUtils.DotProduct(CelestialBodyUtils.CrossProduct(position, semiMajorAxisBasis), orbitNormal) < 0)
{
trueAnomaly = -trueAnomaly;
}
eccentricAnomaly = CelestialBodyUtils.ConvertTrueToEccentricAnomaly(trueAnomaly, eccentricity);
meanAnomaly = System.Math.Sinh(eccentricAnomaly) * eccentricity - eccentricAnomaly;
}
}
