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>
/// When first time called this method makes orbit clockwise, next time - oposite
/// Orbit plane will be unchanged.
/// </summary>
public void MakeOrbitCircle() {
if (attractor) {
#if UNITY_EDITOR
if (!Application.isPlaying) {
FindReferences();
attractor.FindReferences();
Undo.RecordObject(this, "Round orbit");
}
#endif
var v = CelestialBodyUtils.CalcCircleOrbitVelocity(
attractor._position,
_position,
attractor.mass,
mass,
orbitData.orbitNormal,
simControlRef.gravitationalConstant
);
if (relativeVelocity == v) {
relativeVelocity = -v;
} else {
relativeVelocity = v;
}
orbitData.isDirty = true;
}
#if UNITY_EDITOR
else {
Debug.Log("SpaceGravity2D: Can't round orbit. " + name + " has no attractor");
}
#endif
}
/// <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 void SetEccentricAnomaly(double e)
{
if (!isValidOrbit)
{
return;
}
e %= Mathd.PI_2;
eccentricAnomaly = e;
if (eccentricity < 1)
{
if (e < 0)
{
e = Mathd.PI_2 + e;
}
eccentricAnomaly = e;
trueAnomaly = CelestialBodyUtils.ConvertEccentricToTrueAnomaly(e, eccentricity);
meanAnomaly = eccentricAnomaly - eccentricity * System.Math.Sin(eccentricAnomaly);
}
else
{
trueAnomaly = CelestialBodyUtils.ConvertEccentricToTrueAnomaly(e, eccentricity);
meanAnomaly = System.Math.Sinh(eccentricAnomaly) * eccentricity - eccentricAnomaly;
}
SetPositionByCurrentAnomaly();
SetVelocityByCurrentAnomaly();
}
/// <summary>
/// Sets the true anomaly and updates all other anomalies.
/// </summary>
/// <param name="t">The t.</param>
public void SetTrueAnomaly(double t)
{
if (!IsValidOrbit)
{
return;
}
t %= Mathd.PI_2;
if (Eccentricity < 1)
{
if (t < 0)
{
t += Mathd.PI_2;
}
EccentricAnomaly = CelestialBodyUtils.ConvertTrueToEccentricAnomaly(t, Eccentricity);
MeanAnomaly = EccentricAnomaly - Eccentricity * Math.Sin(EccentricAnomaly);
}
else
{
EccentricAnomaly = CelestialBodyUtils.ConvertTrueToEccentricAnomaly(t, Eccentricity);
MeanAnomaly = Math.Sinh(EccentricAnomaly) * Eccentricity - EccentricAnomaly;
}
SetPositionByCurrentAnomaly();
SetVelocityByCurrentAnomaly();
}
/// <summary>
/// Sets the eccentric anomaly and updates all other anomalies.
/// </summary>
/// <param name="e">The e.</param>
public void SetEccentricAnomaly(double e)
{
if (!IsValidOrbit)
{
return;
}
e %= Mathd.PI_2;
EccentricAnomaly = e;
if (Eccentricity < 1)
{
if (e < 0)
{
e = Mathd.PI_2 + e;
}
EccentricAnomaly = e;
TrueAnomaly = CelestialBodyUtils.ConvertEccentricToTrueAnomaly(e, Eccentricity);
MeanAnomaly = EccentricAnomaly - Eccentricity * Math.Sin(EccentricAnomaly);
}
else
{
TrueAnomaly = CelestialBodyUtils.ConvertEccentricToTrueAnomaly(e, Eccentricity);
MeanAnomaly = Math.Sinh(EccentricAnomaly) * Eccentricity - EccentricAnomaly;
}
SetPositionByCurrentAnomaly();
SetVelocityByCurrentAnomaly();
}
private void DrawOrbitInEditorFor(CelestialBody body)
{
int pointsCount = _simControl.SceneElementsDisplayParameters.OrbitPointsCount;
if (body.isActiveAndEnabled)
{
if (!Application.isPlaying && body.AttractorRef != null && body.OrbitData.IsDirty)
{
if (body.AttractorRef.Mass <= 0)
{
body.AttractorRef.Mass = 1e-007;//to avoid div by zero
}
body.CalculateNewOrbitData();
}
Handles.color = Color.white;
Vector3d[] points = null;
body.GetOrbitPointsNoAlloc(ref points, pointsCount, false, (float)_simControl.SceneElementsDisplayParameters.MaxOrbitDistance);
for (int i = 1; i < points.Length; i++)
{
Handles.DrawLine((Vector3)points[i - 1], (Vector3)points[i]);
}
if (_simControl.SceneElementsDisplayParameters.DrawOrbitsEclipticProjection && points.Length > 0)
{
var point1 = points[0] - _simControl.EclipticNormal * CelestialBodyUtils.DotProduct(points[0], _simControl.EclipticNormal);
var point2 = Vector3d.zero;
Handles.color = Color.gray;
for (int i = 1; i < points.Length; i++)
{
point2 = points[i] - _simControl.EclipticNormal * CelestialBodyUtils.DotProduct(points[i], _simControl.EclipticNormal);
Handles.DrawLine((Vector3)point1, (Vector3)point2);
point1 = point2;
}
}
}
}
/// <summary>
/// Orbit plane will be unchanged.
/// </summary>
public void MakeOrbitCircle(bool clockwise) {
if (attractor) {
#if UNITY_EDITOR
if (!Application.isPlaying) {
FindReferences();
attractor.FindReferences();
Undo.RecordObject(this, "Round orbit");
}
#endif
var dotProduct = CelestialBodyUtils.DotProduct(orbitData.orbitNormal, simControlRef.eclipticNormal); //sign of this value determines orbit orientation
if (Mathd.Abs(orbitData.orbitNormal.sqrMagnitude - 1d) > 0.5d) {
orbitData.orbitNormal = simControlRef.eclipticNormal;
}
var v = CelestialBodyUtils.CalcCircleOrbitVelocity(
attractor._position,
_position,
attractor.mass,
mass,
orbitData.orbitNormal * ( clockwise && dotProduct >= 0 || !clockwise && dotProduct < 0 ? 1 : -1 ),
simControlRef.gravitationalConstant
);
if (relativeVelocity != v) {
relativeVelocity = v;
orbitData.isDirty = true;
}
}
}
public void SetTrueAnomaly(double t)
{
if (!isValidOrbit)
{
return;
}
t %= Mathd.PI_2;
if (eccentricity < 1)
{
if (t < 0)
{
t += Mathd.PI_2;
}
eccentricAnomaly = CelestialBodyUtils.ConvertTrueToEccentricAnomaly(t, eccentricity);
meanAnomaly = eccentricAnomaly - eccentricity * System.Math.Sin(eccentricAnomaly);
}
else
{
eccentricAnomaly = CelestialBodyUtils.ConvertTrueToEccentricAnomaly(t, eccentricity);
meanAnomaly = System.Math.Sinh(eccentricAnomaly) * eccentricity - eccentricAnomaly;
}
SetPositionByCurrentAnomaly();
SetVelocityByCurrentAnomaly();
}
/// <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);
}
public void SetAutoCircleOrbit()
{
if (AttractorObjectRef != null)
{
OrbitData.Velocity = CelestialBodyUtils.CalcCircleOrbitVelocity(Vector3d.zero, OrbitData.Position, OrbitData.AttractorMass, 1f, OrbitData.OrbitNormal, OrbitData.GravitationalConstant);
OrbitData.CalculateNewOrbitData();
if (VelocityHandleRef != null)
{
VelocityHandleRef.position = transform.position + (Vector3)OrbitData.Velocity;
}
}
}
/// <summary>
/// Return ratio of perturbation force from third body relative to attraction force of mainAttractor
/// </summary>
/// <param name="targetBody"></param>
/// <param name="mainAttractor"></param>
/// <param name="perturbatingAttractor"></param>
public static double RelativePerturbationRatio(CelestialBody targetBody, CelestialBody mainAttractor, CelestialBody perturbatingAttractor)
{
double mainAcceleration = CelestialBodyUtils.AccelerationByAttractionForce(
targetBody.position,
mainAttractor.position,
mainAttractor.MG).magnitude;
double perturbAcceleration = CelestialBodyUtils.AccelerationByAttractionForce(
targetBody.position,
perturbatingAttractor.position,
perturbatingAttractor.MG).magnitude;
return(perturbAcceleration / mainAcceleration);
}
public static Vector3 GetRayPlaneIntersectionPoint(Vector3 pointOnPlane, Vector3 normal, Vector3 rayOrigin, Vector3 rayDirection)
{
var dotProd = CelestialBodyUtils.DotProduct(rayDirection, normal);
if (Mathd.Abs(dotProd) < 1e-5)
{
return(new Vector3());
}
var p = rayOrigin + rayDirection * CelestialBodyUtils.DotProduct((pointOnPlane - rayOrigin), normal) / dotProd;
p = p - normal * CelestialBodyUtils.DotProduct(p - pointOnPlane, normal); //projection. for better precision
return(p);
}
/// <summary>
/// Get orbit curve points without array allocation, if current orbit state is valid.
/// </summary>
/// <remarks>
/// Note: array allocation may sometimes occur, if specified array is null or lenght is not equal to target points count.
/// </remarks>
/// <param name="points">Resulting orbit curve array.</param>
/// <param name="pointsCount">Max orbit curve points count.</param>
/// <param name="origin">World position of attractor (focus of orbit).</param>
/// <param name="maxDistance">Max distance for orbit curve points.</param>
public void GetOrbitPointsNoAlloc(ref Vector3d[] points, int pointsCount, Vector3d origin, double maxDistance = 1000d)
{
if (pointsCount < 2)
{
points = new Vector3d[0];
return;
}
if (Eccentricity < 1)
{
if (points == null || points.Length != pointsCount)
{
points = new Vector3d[pointsCount];
}
if (ApoapsisDistance < maxDistance)
{
for (var i = 0; i < pointsCount; i++)
{
points[i] = GetFocalPositionAtEccentricAnomaly(i * Mathd.PI_2 / (pointsCount - 1d)) + origin;
}
}
else
{
var maxAngle = CelestialBodyUtils.CalcTrueAnomalyForDistance(maxDistance, Eccentricity, SemiMajorAxis);
for (int i = 0; i < pointsCount; i++)
{
points[i] = GetFocalPositionAtTrueAnomaly(-maxAngle + i * 2d * maxAngle / (pointsCount - 1)) + origin;
}
}
}
else
{
if (maxDistance < PeriapsisDistance)
{
points = new Vector3d[0];
return;
}
if (points == null || points.Length != pointsCount)
{
points = new Vector3d[pointsCount];
}
var maxAngle = CelestialBodyUtils.CalcTrueAnomalyForDistance(maxDistance, Eccentricity, SemiMajorAxis);
for (int i = 0; i < pointsCount; i++)
{
points[i] = GetFocalPositionAtTrueAnomaly(-maxAngle + i * 2d * maxAngle / (pointsCount - 1)) + origin;
}
}
}
/// <summary>
/// Calculate and apply n-body gravitational acceleration to target body, using algorythm Runge-Kutta.
/// In result body will change it's velocity according to global gravity.
/// </summary>
/// <param name="body">Target body.</param>
/// <param name="dt">Delta time.</param>
/// <param name="minRange">Minimal attraction range for attractors.</param>
/// <param name="maxRange">Maximal attraction range for attractors.</param>
/// <param name="allAttractors">List of all attractors on scene.</param>
public static void CalcAccelerationRungeKuttaForBody(CelestialBody body, double dt, double minRange, double maxRange, List <CelestialBody> allAttractors)
{
Vector3d result = Vector3d.zero;
body._position += body.Velocity * (dt / 2d);
for (int i = 0; i < allAttractors.Count; i++)
{
if (allAttractors[i] == body)
{
continue;
}
var t1 = CelestialBodyUtils.AccelerationByAttractionForce(
body._position,
allAttractors[i].Position,
allAttractors[i].MG,
minRange,
Mathd.Min(maxRange, allAttractors[i].MaxAttractionRange)
) * dt;
var t2 = CelestialBodyUtils.AccelerationByAttractionForce(
body._position + t1 * 0.5d,
allAttractors[i].Position,
allAttractors[i].MG,
minRange,
Mathd.Min(maxRange, allAttractors[i].MaxAttractionRange)
) * dt;
var t3 = CelestialBodyUtils.AccelerationByAttractionForce(
body._position + t2 * 0.5d,
allAttractors[i].Position,
allAttractors[i].MG,
minRange,
Mathd.Min(maxRange, allAttractors[i].MaxAttractionRange)
) * dt;
var t4 = CelestialBodyUtils.AccelerationByAttractionForce(
body._position + t3,
allAttractors[i].Position,
allAttractors[i].MG,
minRange,
Mathd.Min(maxRange, allAttractors[i].MaxAttractionRange)
) * dt;
result += new Vector3d(
(t1.x + t2.x * 2d + t3.x * 2d + t4.x) / 6d,
(t1.y + t2.y * 2d + t3.y * 2d + t4.y) / 6d,
(t1.z + t2.z * 2d + t3.z * 2d + t4.z) / 6d);
}
if (!result.isZero)
{
body.Velocity += result;
}
}
public CelestialBody FindMostProperAttractor(CelestialBody body)
{
if (body == null)
{
return(null);
}
CelestialBody resultAttractor = null;
#if UNITY_EDITOR
if (!Application.isPlaying)
{
bodies = new List <CelestialBody>(GameObject.FindObjectsOfType <CelestialBody>());
}
#endif
// Search logic:
// calculate mutual perturbation for every pair of attractors in scene and select one,
// which attracts the body with biggest force and is least affected by others.
foreach (var otherBody in bodies)
{
if (otherBody == body || !otherBody.isActiveAndEnabled || otherBody.mass < minAttractorMass || (otherBody.position - body.position).magnitude > Mathd.Min(maxAttractionRange, otherBody.maxAttractionRange))
{
continue;
}
#if UNITY_EDITOR
if (!Application.isPlaying)
{
otherBody.FindReferences();
}
#endif
if (resultAttractor == null)
{
resultAttractor = otherBody;
}
else
if (CelestialBodyUtils.RelativePerturbationRatio(body, resultAttractor, otherBody) > CelestialBodyUtils.RelativePerturbationRatio(body, otherBody, resultAttractor))
{
resultAttractor = otherBody;
}
}
#if UNITY_EDITOR
if (!Application.isPlaying)
{
bodies.Clear(); //bodies must be empty in editor mode
}
#endif
return(resultAttractor);
}
/// <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;
}
public void CalcAccelerationRungeKuttaForBody(CelestialBody body, double dt)
{
Vector3d result = Vector3d.zero;
body._position += body.velocity * (dt / 2d);
for (int i = 0; i < attractorsCache.Count; i++)
{
if (attractorsCache[i] == body)
{
continue;
}
var t1 = CelestialBodyUtils.AccelerationByAttractionForce(
body._position,
attractorsCache[i].position,
attractorsCache[i].MG,
minAttractionRange,
Mathd.Min(maxAttractionRange, attractorsCache[i].maxAttractionRange)
) * dt;
var t2 = CelestialBodyUtils.AccelerationByAttractionForce(
body._position + t1 * 0.5d,
attractorsCache[i].position,
attractorsCache[i].MG,
minAttractionRange,
Mathd.Min(maxAttractionRange, attractorsCache[i].maxAttractionRange)
) * dt;
var t3 = CelestialBodyUtils.AccelerationByAttractionForce(
body._position + t2 * 0.5d,
attractorsCache[i].position,
attractorsCache[i].MG,
minAttractionRange,
Mathd.Min(maxAttractionRange, attractorsCache[i].maxAttractionRange)
) * dt;
var t4 = CelestialBodyUtils.AccelerationByAttractionForce(
body._position + t3,
attractorsCache[i].position,
attractorsCache[i].MG,
minAttractionRange,
Mathd.Min(maxAttractionRange, attractorsCache[i].maxAttractionRange)
) * dt;
result += new Vector3d(
(t1.x + t2.x * 2d + t3.x * 2d + t4.x) / 6d,
(t1.y + t2.y * 2d + t3.y * 2d + t4.y) / 6d,
(t1.z + t2.z * 2d + t3.z * 2d + t4.z) / 6d);
}
body.velocity += result;
}
/// <summary>
/// Updates the value of orbital anomalies by defined deltatime.
/// </summary>
/// <param name="deltaTime">The delta time.</param>
/// <remarks>
/// Only anomalies values will be changed.
/// Position and velocity states needs to be updated too after this method call.
/// </remarks>
public void UpdateOrbitAnomaliesByTime(double deltaTime)
{
if (Eccentricity < 1)
{
if (Period > 1e-5)
{
MeanAnomaly += Mathd.PI_2 * deltaTime / Period;
}
MeanAnomaly %= Mathd.PI_2;
if (MeanAnomaly < 0)
{
MeanAnomaly = Mathd.PI_2 - MeanAnomaly;
}
EccentricAnomaly = CelestialBodyUtils.KeplerSolver(MeanAnomaly, Eccentricity);
var cosE = Math.Cos(EccentricAnomaly);
TrueAnomaly = Math.Acos((cosE - Eccentricity) / (1 - Eccentricity * cosE));
if (MeanAnomaly > Mathd.PI)
{
TrueAnomaly = Mathd.PI_2 - TrueAnomaly;
}
if (double.IsNaN(MeanAnomaly) || double.IsInfinity(MeanAnomaly))
{
Debug.Log("SpaceGravity2D: NaN(INF) MEAN ANOMALY"); //litle paranoya
Debug.Break();
}
if (double.IsNaN(EccentricAnomaly) || double.IsInfinity(EccentricAnomaly))
{
Debug.Log("SpaceGravity2D: NaN(INF) ECC ANOMALY");
Debug.Break();
}
if (double.IsNaN(TrueAnomaly) || double.IsInfinity(TrueAnomaly))
{
Debug.Log("SpaceGravity2D: NaN(INF) TRUE ANOMALY");
Debug.Break();
}
}
else
{
double n = Math.Sqrt(AttractorMass * GravitationalConstant / Math.Pow(SemiMajorAxis, 3));
MeanAnomaly = MeanAnomaly + n * deltaTime;
EccentricAnomaly = CelestialBodyUtils.KeplerSolverHyperbolicCase(MeanAnomaly, Eccentricity);
TrueAnomaly = Math.Atan2(Math.Sqrt(Eccentricity * Eccentricity - 1.0) * Math.Sinh(EccentricAnomaly), Eccentricity - Math.Cosh(EccentricAnomaly));
}
}
/// <summary>
/// Find attractor, which have most gravitational influence at target body.
/// </summary>
/// <param name="body">Target body.</param>
/// <returns>Most proper attractor or null.</returns>
/// <remarks>
/// Search logic:
/// Calculate mutual perturbation for every pair of attractors in scene and select one,
/// which attracts the body with biggest force and is least affected by others.
/// </remarks>
public CelestialBody FindMostProperAttractor(CelestialBody body)
{
if (body == null)
{
return(null);
}
CelestialBody resultAttractor = null;
#if UNITY_EDITOR
if (!Application.isPlaying)
{
Bodies = new List <CelestialBody>(GameObject.FindObjectsOfType <CelestialBody>());
}
#endif
foreach (var otherBody in Bodies)
{
if (otherBody == body || !otherBody.isActiveAndEnabled || otherBody.Mass < MinAttractorMass || (otherBody.Position - body.Position).magnitude > Mathd.Min(MaxAttractionRange, otherBody.MaxAttractionRange))
{
continue;
}
#if UNITY_EDITOR
if (!Application.isPlaying)
{
otherBody.FindReferences();
}
#endif
if (resultAttractor == null)
{
resultAttractor = otherBody;
}
else
if (CelestialBodyUtils.RelativePerturbationRatio(body, resultAttractor, otherBody) > CelestialBodyUtils.RelativePerturbationRatio(body, otherBody, resultAttractor))
{
resultAttractor = otherBody;
}
}
#if UNITY_EDITOR
if (!Application.isPlaying)
{
Bodies.Clear(); //bodies must be empty in editor mode
}
#endif
return(resultAttractor);
}
public void UpdateOrbitAnomaliesByTime(double deltaTime)
{
if (eccentricity < 1)
{
if (period > 1e-5)
{
meanAnomaly += Mathd.PI_2 * deltaTime / period;
}
meanAnomaly %= Mathd.PI_2;
if (meanAnomaly < 0)
{
meanAnomaly = Mathd.PI_2 - meanAnomaly;
}
eccentricAnomaly = CelestialBodyUtils.KeplerSolver(meanAnomaly, eccentricity);
var cosE = System.Math.Cos(eccentricAnomaly);
trueAnomaly = System.Math.Acos((cosE - eccentricity) / (1 - eccentricity * cosE));
if (meanAnomaly > Mathd.PI)
{
trueAnomaly = Mathd.PI_2 - trueAnomaly;
}
if (double.IsNaN(meanAnomaly) || double.IsInfinity(meanAnomaly))
{
Debug.Log("SpaceGravity2D: NaN(INF) MEAN ANOMALY"); //litle paranoya
Debug.Break();
}
if (double.IsNaN(eccentricAnomaly) || double.IsInfinity(eccentricAnomaly))
{
Debug.Log("SpaceGravity2D: NaN(INF) ECC ANOMALY");
Debug.Break();
}
if (double.IsNaN(trueAnomaly) || double.IsInfinity(trueAnomaly))
{
Debug.Log("SpaceGravity2D: NaN(INF) TRUE ANOMALY");
Debug.Break();
}
}
else
{
double n = System.Math.Sqrt(attractorMass * gravConst / System.Math.Pow(semiMajorAxis, 3)) * Mathd.Sign(orbitNormalDotEclipticNormal);
meanAnomaly = meanAnomaly - n * deltaTime;
eccentricAnomaly = CelestialBodyUtils.KeplerSolverHyperbolicCase(meanAnomaly, eccentricity);
trueAnomaly = System.Math.Atan2(System.Math.Sqrt(eccentricity * eccentricity - 1.0) * System.Math.Sinh(eccentricAnomaly), eccentricity - System.Math.Cosh(eccentricAnomaly));
}
}
public void ProjectOntoEclipticPlane() {
#if UNITY_EDITOR
if (!Application.isPlaying) {
Undo.RecordObject(this, "ecliptic projection");
Undo.RecordObject(transformRef, "ecliptic projection");
}
#endif
var projectedPos = _position - simControlRef.eclipticNormal * CelestialBodyUtils.DotProduct(_position, simControlRef.eclipticNormal);
var projectedV = velocity - simControlRef.eclipticNormal * CelestialBodyUtils.DotProduct(velocity, simControlRef.eclipticNormal);
_position = projectedPos;
transformRef.position = (Vector3)projectedPos;
velocity = projectedV;
orbitData.isDirty = true;
#if UNITY_EDITOR
if (!Application.isPlaying) {
EditorUtility.SetDirty(this);
}
#endif
}
public void CalcAccelerationEulerForBody(CelestialBody body, double dt)
{
Vector3d result = Vector3d.zero;
for (int i = 0; i < attractorsCache.Count; i++)
{
if (attractorsCache[i] == body)
{
continue;
}
result += CelestialBodyUtils.AccelerationByAttractionForce(
body.position,
attractorsCache[i].position,
attractorsCache[i].MG,
minAttractionRange,
Mathd.Min(maxAttractionRange, attractorsCache[i].maxAttractionRange)
);
}
body.velocity += result * dt;
}
public Vector3d CalcAccelerationEulerInPoint(Vector3d pos)
{
Vector3d result = new Vector3d();
for (int i = 0; i < attractorsCache.Count; i++)
{
if (attractorsCache[i].position == pos)
{
continue;
}
result += CelestialBodyUtils.AccelerationByAttractionForce(
pos,
attractorsCache[i].position,
attractorsCache[i].MG,
minAttractionRange,
Mathd.Min(maxAttractionRange, attractorsCache[i].maxAttractionRange)
);
}
return(result);
}
/// <summary>
/// Calculate n-body gravitational acceleration at specified world point, using Euler algorythm.
/// </summary>
/// <param name="pos">World position.</param>
/// <param name="minRange">Minimal attraction range for attractors.</param>
/// <param name="maxRange">Maximal attraction range for attractors.</param>
/// <param name="allAttractors">List of all attractors on scene.</param>
/// <returns>Sum of accelerations vectors at position.</returns>
public static Vector3d CalcAccelerationEulerInPoint(Vector3d pos, double minRange, double maxRange, List <CelestialBody> allAttractors)
{
Vector3d result = new Vector3d();
for (int i = 0; i < allAttractors.Count; i++)
{
if (allAttractors[i].Position == pos)
{
continue;
}
result += CelestialBodyUtils.AccelerationByAttractionForce(
pos,
allAttractors[i].Position,
allAttractors[i].MG,
minRange,
Mathd.Min(maxRange, allAttractors[i].MaxAttractionRange)
);
}
return(result);
}
public Vector3[] GetOrbitPoints(int pointsCount, Vector3 origin, float maxDistance = 1000f)
{
if (pointsCount < 2)
{
return(new Vector3[0]);
}
var result = new Vector3[pointsCount];
if (eccentricity < 1)
{
if (apoapsisDistance < maxDistance)
{
for (var i = 0; i < pointsCount; i++)
{
result[i] = (Vector3)GetFocalPositionAtEccentricAnomaly(i * Mathd.PI_2 / (pointsCount - 1d)) + origin;
}
}
else
{
var maxAngle = CelestialBodyUtils.CalcTrueAnomalyForDistance(maxDistance, eccentricity, semiMajorAxis);
for (int i = 0; i < pointsCount; i++)
{
result[i] = (Vector3)GetFocalPositionAtTrueAnomaly(-maxAngle + i * 2d * maxAngle / (pointsCount - 1)) + origin;
}
}
}
else
{
if (maxDistance < periapsisDistance)
{
return(new Vector3[0]);
}
var maxAngle = CelestialBodyUtils.CalcTrueAnomalyForDistance(maxDistance, eccentricity, semiMajorAxis);
for (int i = 0; i < pointsCount; i++)
{
result[i] = (Vector3)GetFocalPositionAtTrueAnomaly(-maxAngle + i * 2d * maxAngle / (pointsCount - 1)) + origin;
}
}
return(result);
}
/// <summary>
/// Calculate and apply n-body gravitational acceleration to target body, using Euler algorythm.
/// In result body will change it's velocity according to global gravity.
/// </summary>
/// <param name="body">Target body.</param>
/// <param name="dt">Delta time.</param>
/// <param name="minRange">Minimal attraction range for attractors.</param>
/// <param name="maxRange">Maximal attraction range for attractors.</param>
/// <param name="allAttractors">List of all attractors on scene.</param>
public static void CalcAccelerationEulerForBody(CelestialBody body, double dt, double minRange, double maxRange, List <CelestialBody> allAttractors)
{
Vector3d result = Vector3d.zero;
for (int i = 0; i < allAttractors.Count; i++)
{
if (object.ReferenceEquals(allAttractors[i], body))
{
continue;
}
result += CelestialBodyUtils.AccelerationByAttractionForce(
body.Position,
allAttractors[i].Position,
allAttractors[i].MG,
minRange,
Mathd.Min(maxRange, allAttractors[i].MaxAttractionRange)
);
}
if (!result.isZero)
{
body.Velocity += result * dt;
}
}
/// <summary>
/// Sets the mean anomaly and updates all other anomalies.
/// </summary>
/// <param name="m">The m.</param>
public void SetMeanAnomaly(double m)
{
if (!IsValidOrbit)
{
return;
}
MeanAnomaly = m % Mathd.PI_2;
if (Eccentricity < 1)
{
if (MeanAnomaly < 0)
{
MeanAnomaly += Mathd.PI_2;
}
EccentricAnomaly = CelestialBodyUtils.KeplerSolver(MeanAnomaly, Eccentricity);
TrueAnomaly = CelestialBodyUtils.ConvertEccentricToTrueAnomaly(EccentricAnomaly, Eccentricity);
}
else
{
EccentricAnomaly = CelestialBodyUtils.KeplerSolverHyperbolicCase(MeanAnomaly, Eccentricity);
TrueAnomaly = CelestialBodyUtils.ConvertEccentricToTrueAnomaly(EccentricAnomaly, Eccentricity);
}
SetPositionByCurrentAnomaly();
SetVelocityByCurrentAnomaly();
}