// Evolve the dynamical system using a 4th order RK integrator
private Vector3 Evolve(float h)
{
Vector3 xout = Vector3.zero;
chaosEqn.Function(ref x, ref a_n);
float h_frac = h / 2f;
arg[0] = x[0] + h_frac * a_n[0];
arg[1] = x[1] + h_frac * a_n[1];
arg[2] = x[2] + h_frac * a_n[2];
chaosEqn.Function(ref arg, ref b_n);
arg[0] = x[0] + h_frac * b_n[0];
arg[1] = x[1] + h_frac * b_n[1];
arg[2] = x[2] + h_frac * b_n[2];
chaosEqn.Function(ref arg, ref c_n);
h_frac = h;
arg[0] = x[0] + h_frac * c_n[0];
arg[1] = x[1] + h_frac * c_n[1];
arg[2] = x[2] + h_frac * c_n[2];
chaosEqn.Function(ref arg, ref d_n);
h_frac = h / 6f;
xout.x = x[0] + h_frac * (a_n[0] + 2f * b_n[0] + 2f * c_n[0] + d_n[0]);
xout.y = x[1] + h_frac * (a_n[1] + 2f * b_n[1] + 2f * c_n[1] + d_n[1]);
xout.z = x[2] + h_frac * (a_n[2] + 2f * b_n[2] + 2f * c_n[2] + d_n[2]);
x[0] = xout.x;
x[1] = xout.y;
x[2] = xout.z;
return(xout);
}
// Evolve the dynamical system using a 4th order RK integrator
private void Evolve(float h)
{
// do nothing if all inactive
if (inactive == null)
{
return; // Particle system has not init-ed yet or is done
}
// (did not work in Start() -> Unity bug? Init sequencing?)
if (!playing)
{
chaosParticles.Play();
playing = true;
}
for (int j = 0; j < particleCount; j++)
{
if (!inactive[j])
{
Vector3 xout = Vector3.zero;
x_in[0] = x[j, 0];
x_in[1] = x[j, 1];
x_in[2] = x[j, 2];
chaosEqn.Function(ref x_in, ref a_n);
//Debug.Log("j=" + j + " x=" + x[j,0] + " arg0=" + arg[0] + " a_n0=" + a_n[0]);
float h_frac = h / 2f;
arg[0] = x[j, 0] + h_frac * a_n[0];
arg[1] = x[j, 1] + h_frac * a_n[1];
arg[2] = x[j, 2] + h_frac * a_n[2];
chaosEqn.Function(ref arg, ref b_n);
arg[0] = x[j, 0] + h_frac * b_n[0];
arg[1] = x[j, 1] + h_frac * b_n[1];
arg[2] = x[j, 2] + h_frac * b_n[2];
chaosEqn.Function(ref arg, ref c_n);
h_frac = h;
arg[0] = x[j, 0] + h_frac * c_n[0];
arg[1] = x[j, 1] + h_frac * c_n[1];
arg[2] = x[j, 2] + h_frac * c_n[2];
chaosEqn.Function(ref arg, ref d_n);
h_frac = h / 6f;
x[j, 0] = x[j, 0] + h_frac * (a_n[0] + 2f * b_n[0] + 2f * c_n[0] + d_n[0]);
x[j, 1] = x[j, 1] + h_frac * (a_n[1] + 2f * b_n[1] + 2f * c_n[1] + d_n[1]);
x[j, 2] = x[j, 2] + h_frac * (a_n[2] + 2f * b_n[2] + 2f * c_n[2] + d_n[2]);
if (double.IsNaN(x[j, 0]) || double.IsNaN(x[j, 1]) || double.IsNaN(x[j, 2]))
{
inactive[j] = true;
}
}
}
}
