public static void RK4Integrate(ref Vector3d position, ref Vector3d velocity, double dt,
PlanetRigidbody self, PlanetAggregator aggr)
{
Vector3d p1, p2, p3, p4;
Vector3d v1, v2, v3, v4;
Vector3d a1, a2, a3, a4;
p1 = position;
v1 = velocity;
a1 = aggr.ComputeNetGravity(p1, self);
p2 = position + 0.5 * v1 * dt;
v2 = velocity + 0.5 * a1 * dt;
a2 = aggr.ComputeNetGravity(p2, self);
p3 = position + 0.5 * v2 * dt;
v3 = velocity + 0.5 * a2 * dt;
a3 = aggr.ComputeNetGravity(p3, self);
p4 = position + v3 * dt;
v4 = velocity + a3 * dt;
a4 = aggr.ComputeNetGravity(p4, self);
position += (dt / 6.0) * (v1 + 2.0 * v2 + 2.0 * v3 + v4);
velocity += (dt / 6.0) * (a1 + 2.0 * a2 + 2.0 * a3 + a4);
}
public static void MeanAccelerationIntegrate(ref Vector3d position, ref Vector3d velocity, Vector3d acceleration, double dt,
PlanetRigidbody self, PlanetAggregator aggr)
{
Vector3d expected_position = position + (velocity * dt);
Vector3d expected_acceleration = aggr.ComputeNetGravity(expected_position, self);
Vector3d new_velocity = velocity + (0.5 * (acceleration + expected_acceleration) * dt);
position += 0.5 * (velocity + new_velocity) * dt;
velocity = new_velocity;
}
public Vector3d ComputeNetGravity(Vector3d position, PlanetRigidbody self)
{
Vector3d net = Vector3d.zero;
foreach (PlanetRigidbody body in bodies)
{
if (body != self)
{
net += ComputeGravityForce(position, body);
}
}
return(net);
}
void Draw()
{
// do this kind of iterative thing to do the arc sweeps
List <Vector3> positions = new List <Vector3>();
Vector3d position = new Vector3d(transform.position);
Vector3d velocity = new Vector3d(transform.forward * speed);
Vector3d acceleration = Vector3d.zero;
positions.Add(position.ToVector3());
for (int i = 0; i < steps; i++)
{
//acceleration = aggregator.ComputeNetGravity(position, planet);
PlanetRigidbody.RK4Integrate(ref position, ref velocity, timestep, planet, aggregator);
positions.Add(position.ToVector3());
}
trajectory.positionCount = positions.Count;
trajectory.SetPositions(positions.ToArray());
}
public Vector3d ComputeGravityForce(Vector3d position, PlanetRigidbody body)
{
Vector3d body_pos = new Vector3d(
(double)body.transform.position.x,
(double)body.transform.position.y,
(double)body.transform.position.z
);
double r = Vector3d.SqrDistance(position, body_pos);
// I'm fine with this approximation because it solves the problem of the div by zero of
// objects trying to attract themselves, and two objects centers overlapping is pretty nonsense
// conceptually
if (r <= Vector3d.MIN_DOUBLE)
{
return(Vector3d.zero);
}
double a = (double)body.mass / r;
return((body_pos - position).normalized * a);
}
void Awake()
{
aggregator = GameObject.Find("Planet Aggregator").GetComponent <PlanetAggregator>();
planet = GetComponent <PlanetRigidbody>();
trajectory = GetComponent <LineRenderer>();
}
// Here we assume constant acceleration for the duration of the timestep
public static void EulerIntegrate(ref Vector3d position, ref Vector3d velocity, Vector3d acceleration, double dt,
PlanetRigidbody self, PlanetAggregator aggr)
{
velocity += acceleration * dt;
position += velocity * dt;
}
