/*
*
* function phase_space_state = get_phase_space_state (Particle_System)
* %GET_PHASE_SPACE_STATE Retrieve phase space state vector.
* %
* % Example
* %
* % SS = GET_PHASE_SPACE_STATE (PS) returns the current 1-by-6*N
* % phase space state vector SS from the particle system PS.
* % N is the number of particles.
* %
* % See also set_phase_space_state.
* %
* % Copyright 2008-2008 buchholz.hs-bremen.de
*
* positions = get_particles_positions (Particle_System);
* velocities = get_particles_velocities (Particle_System);
*
* phase_space_state = [positions, velocities];
*
* end
*
*/
// see the pdf page 56. quuestion about ode4. claims this is called 4 times by that.
//function state_derivative = compute_state_derivative ...
//(time , phase_space_state , Particle_System )
// so i supose i have to pass in tiem, parentsystem and phasestate too
//private List<PhaseSpace> computeStateDerivate(List<PhaseSpace> phaseSpaceStates) //not sure time needed // herein lays the problem
//{
// List<PhaseSpace> stateDerivate = null;
// //if (this.currentPhaseSpace != null)
// {
// //the matlab code sets phaseSpace here before updateing forces.
// /*
// The evaluation is initialized by transposing the state vector into a row30 vector
// phase_space_state = phase_space_state (:) ’;
// and inserting it (back) into the particle system
// Particle_System . set_phase_space_state ( phase_space_state );
// */
// // this.setPhaseSpace(this.currentPhaseSpace); //added in atempt to fix the above // but sends the partilce flying into the air
// this.setPhaseSpace(phaseSpaceStates);
// updateAllForces(); // should this really update forces? i nkow the matlab does. but the pixar didn't // maybe it a problem i don't have attractions yet
// stateDerivate = new List<PhaseSpace>();
// List<Vector3> _velocities = getParticlesVelocities();
// List<Vector3> _accelerations = getParticlesAccelerations();
// if ((_velocities == null || _accelerations == null) || (_velocities.Count != this.particles.Count || _accelerations.Count != this.particles.Count))
// {
// Debug.LogWarning("ERROR: velocities, accelerations and Particles lists are not same length or null!!");
// }
// else
// {
// for (int i = 0; i < this.particles.Count; i++)
// {
// if (this.particles[i] != null)
// {
// stateDerivate.Add(new PhaseSpace());
// stateDerivate[i].x = _velocities[i].x;
// stateDerivate[i].y = _velocities[i].y;
// stateDerivate[i].z = _velocities[i].z;
// stateDerivate[i].x_v = _accelerations[i].x;
// stateDerivate[i].y_v = _accelerations[i].y;
// stateDerivate[i].z_v = _accelerations[i].z; // that are thise used for anyway? can see where they are used / now they are for drag
// }
// }
// }
// }
// return stateDerivate;
//}
/*
* function state_derivative = compute_state_derivative ...
* (time, phase_space_state, Particle_System)
* %COMPUTE_STATE_DERIVATIVE Compute state derivative vector.
* %
* % Example
* %
* % SD = COMPUTE_STATE_DERIVATIVE (T, SS, PS) returns the 6*N-by-1
* % phase space state derivative vector SD of the particle system PS at time T.
* % SS is the current 6*N-by-1 phase space state vector.
* % N is the number of particles.
* %
* % See also ode4, set_phase_space_state, aggregate_forces,
* % get_particles_velocities, get_particles_accelerations.
* %
* % Copyright 2008-2008 buchholz.hs-bremen.de
*
* phase_space_state = phase_space_state(:)';
*
* Particle_System.set_phase_space_state (phase_space_state);
*
* Particle_System.aggregate_forces;
*
* velocities = Particle_System.get_particles_velocities;
*
* accelerations = Particle_System.get_particles_accelerations;
*
* state_derivative = [velocities, accelerations]';
*
* end
*
*/
public float rungeKutta(PhaseSpace devState, PhaseSpace currentState, float startTime, float endTime, func func)
{
// atm asuming its worknig only doing ode4 in x.pos
float stepTime = endTime - startTime;
float x0 = currentState.x;
float t0 = startTime;
float k1_x = stepTime * func(x0, t0);
float k2_x = stepTime * func(x0 + (k1_x / 2), t0 + (stepTime / 2));
float k3_x = stepTime * func(x0 + (k2_x / 2), t0 + (stepTime / 2));
float k4_x = stepTime * func(x0 + k3_x, t0 + stepTime);
float rk_x = x0 + (1 / 6 * k1_x) + (1 / 3 * k2_x) + (1 / 3 * k3_x) + (1 / 6 * k4_x);
return(rk_x);
/* runge-kutta form pdf page 7
*
*
* h = time step
*
* k1 = h * f(x0, t0)
*
* k2 = h * f(x0 + k1/2 , t0 + h/2)
*
* k3 = h * f(x0 + k2/2 , t0 + h/2)
*
* k4 = h * f(x0 + k3 , t0 + h)
*
* x0(t0+h) = x0 + (1/6 * k1) + (1/3 * k2) +(1/3 * k3) +(1/6 * k4)
*
* The simplest numerical method is called Euler’s method. Let our initial value for x be denoted by
* x0 = x(t0) and our estimate of x at a later time t0 + h by x(t0 + h) where h is a stepsize parameter.
* Euler’s method simply computes x.t0 C h/ by taking a step in the derivative direction,
* x(t0 + h) = x0 + h x'(t0):
*
* x' = f(x,t)
*
* x'' = f/m
*
* v' = f/m
*
* x' = v
*
* which for me means
*
*/
}
private List <PhaseSpace> computeStateDerivate2(List <PhaseSpace> spaceState)
{
this.setPhaseSpace(spaceState);
this.updateAllForces(); // aggregate forces
var velocities = this.getParticlesVelocities();
var accelerations = this.getParticlesAccelerations();
var stateDerivate = new List <PhaseSpace>(this.particles.Count);
for (int i = 0; i < this.particles.Count; i++)
{
var state = new PhaseSpace(velocities[i], accelerations[i]);
stateDerivate.Add(state);
}
return(stateDerivate);
}