/// <summary>Compute static properties for orbit shape and speed</summary>
public void ComputeStaticProperties()
{
orientation = Kepler.ComputeOrientation(argument, longitude, inclination);
semiLatusRectum = Kepler.ComputeSemiLatusRectum(_periapsis, _eccentricity);
semiMajorAxis = Kepler.ComputeSemiMajorAxis(_periapsis, _eccentricity);
rate = Kepler.ComputeRate(_period, _limits.x * Deg2Rad, _limits.y * Deg2Rad);
}
public void UpdateSimulation()
{
if (orbitDecay != 0)
{
orbit.periapsis += orbitDecay * Time.deltaTime * orbit.timeScale;
if (orbit.periapsis <= 0)
{
//behaviour beyond this point is undefined, best not upset the Kraken
ResetSimulation();
StopSimulation();
orbit.StopSimulation();
}
else
{
orbit.period = Math.Sqrt(
(periodOriginal * periodOriginal) *
(orbit.periapsis * orbit.periapsis * orbit.periapsis) /
(semiMajorAxisOriginal * semiMajorAxisOriginal * semiMajorAxisOriginal)
);
}
}
if (apsidalPrecession != 0)
{
orbit.argument = Kepler.WrapAngle(orbit.argument - apsidalPrecession * Time.deltaTime * (float)orbit.timeScale, -180, 180);
}
}
/// <summary>
/// Computes the position of a celestial body on it's orbit at a given time.
/// </summary>
/// <param name="time">Time offset relative to J2000 (1st January 2000) in years.</param>
/// <returns>The position of the celestial body.</returns>
public UnityEngine.Vector3 Position(float time)
{
var a = Elements.MajorRadius;
var lambda = Elements.MeanLongitudeAtEpoch;
var e = Elements.Eccentricity;
var I = Elements.InclinationToElliptic / 180.0 * Math.PI;
var omega = Elements.LongitudeOfPerihelion / 180.0 * Math.PI;
var Omega = Elements.LongitudeOfAscendingNode / 180.0 * Math.PI;
var T = Elements.OrbitalPeriod;
var n = 2.0 * Math.PI / T;
var theta = (lambda + omega) / n;
var M = n * (time - theta);
var E = Kepler.EccentricAnomaly(e, M);
var Theta = 2.0 * Math.Atan(Math.Sqrt((1.0 + e) / (1.0 - e)) * Math.Tan(E / 2.0));
var r = a * (1.0 - e * Math.Cos(E));
var position = new UnityEngine.Vector3(
Convert.ToSingle(r * (Math.Cos(Omega) * Math.Cos(omega + Theta) - Math.Sin(Omega) * Math.Sin(omega + Theta) * Math.Cos(I))),
Convert.ToSingle(r * Math.Sin(omega + Theta) * Math.Sin(I)),
Convert.ToSingle(r * (Math.Sin(Omega) * Math.Cos(omega + Theta) + Math.Cos(Omega) * Math.Sin(omega + Theta) * Math.Cos(I)))
);
return(position);
}
/// <summary>Compute dynamic properties that change over the anomaly</summary>
/// <param name="M">The anomaly to evaluate properties at</param>
public void ComputeDynamicProperties(double M)
{
eccentricAnomaly = Kepler.ComputeEccentricAnomaly(M, _eccentricity);
trueAnomaly = Kepler.ComputeTrueAnomaly(eccentricAnomaly, _eccentricity);
radius = Kepler.ComputeRadius(semiLatusRectum, _eccentricity, trueAnomaly);
position = orientation * Kepler.ComputePosition(radius, trueAnomaly);
velocity = orientation * Kepler.ComputeVelocity(_periapsis, radius, rate, eccentricAnomaly, trueAnomaly, _eccentricity);
}
void OnDrawGizmosSelected()
{
//OnValidate should always be called before this, meaning appropriate values for properties are available
//variables required
Vector3[] path = new Vector3[51];
Vector3 periapsisV = orientation * Vector3.right * (float)_periapsis;
Vector3 positionV = orientation * Kepler.ComputePosition(Kepler.ComputeRadius(semiLatusRectum, _eccentricity, trueAnomaly), trueAnomaly);
//elliptical and circular
//build list of vectors for path
double step, lower, upper;
double r;
lower = Kepler.ComputeTrueAnomaly(Kepler.ComputeEccentricAnomaly(_limits.x * Deg2Rad, _eccentricity), _eccentricity);
upper = Kepler.ComputeTrueAnomaly(Kepler.ComputeEccentricAnomaly(_limits.y * Deg2Rad, _eccentricity), _eccentricity);
step = (upper - lower) / 50;
for (int i = 0; i <= 50; i++)
{
r = Kepler.ComputeRadius(semiLatusRectum, _eccentricity, lower + i * step);
path[i] = Kepler.ComputePosition(r, lower + i * step);
}
//Set the gizmos to draw in parent space
Gizmos.matrix = (transform.parent)? transform.parent.localToWorldMatrix : Matrix4x4.identity;
//draw the path of the orbit
Gizmos.color = Color.cyan;
for (int i = 0; i < 50; i++)
{
Gizmos.DrawLine(orientation * path[i], orientation * path[i + 1]);
}
//draw periapsis vector
Gizmos.DrawLine(Vector3.zero, periapsisV);
//draw position vector
Gizmos.color = Color.blue;
Gizmos.DrawLine(Vector3.zero, positionV);
//draw velocity vector
Gizmos.color = Color.magenta;
Gizmos.DrawLine(positionV, positionV + velocity);
}
void OnEnable()
{
if (orbit == null)
{
line.SetVertexCount(0);
}
else
{
double step, lower, upper, r;
Matrix4x4 matrix = (transform.parent)? transform.parent.localToWorldMatrix : Matrix4x4.identity;
line.SetVertexCount(segments + 1);
upper = Kepler.ComputeTrueAnomaly(Kepler.ComputeEccentricAnomaly(orbit.limits.x * Deg2Rad, orbit.eccentricity), orbit.eccentricity);
lower = Kepler.ComputeTrueAnomaly(Kepler.ComputeEccentricAnomaly(orbit.limits.y * Deg2Rad, orbit.eccentricity), orbit.eccentricity);
step = (upper - lower) / segments;
for (int i = 0; i < segments + 1; i++)
{
r = Kepler.ComputeRadius(orbit.semiLatusRectum, orbit.eccentricity, lower + step * i);
line.SetPosition(i, matrix.MultiplyPoint(orbit.orientation * Kepler.ComputePosition(r, lower + step * i)));
}
}
}
public void UpdateSimulation()
{
angle = Kepler.WrapAngle(angle + Time.deltaTime * rate * timeScale, 0, 2 * Math.PI);
ComputeDynamicProperties(angle);
transform.localRotation = rotation;
}
public void ResetSimulation()
{
angle = Kepler.WrapAngle(meanAngle * Deg2Rad + startEpoch * rate, 0, 2 * Math.PI);
}
/// <summary>Compute dynamic properties that change over the angle</summary>
/// <param name="M">The angle to evaluate properties at</param>
public void ComputeDynamicProperties(double angle)
{
rotation = Kepler.ComputeRotation(axis, angle / Deg2Rad);
}
/// <summary>Computes static properties for rotational axis and speed</summary>
public void ComputeStaticProperties()
{
axis = Kepler.ComputeAxis(_rightAscension, _declination);
rate = Kepler.ComputeRate(_period, -Math.PI, Math.PI);
}