void Simulation::integrateExplicitEuler()
{
VectorX force;
computeForces(m_mesh->m_current_positions, force);
VectorX pos_next;
pos_next.resize(m_mesh->m_system_dimension);
//two explicit euler different modes:
if (m_integration_method == INTEGRATION_EXPLICIT_EULER_DISCRETE)
{
//update rule here is xn+1 = xn + m_h*(vn-1 + f(xn-1,vn-1))
pos_next = m_mesh->m_current_positions +m_h*(m_mesh->m_previous_velocities + force*m_h);
}
else if (m_integration_method == INTEGRATION_EXPLICIT_EULER_SYMPLETIC)
{
//Sympletic Euler uses the new velocity when computing for the new position
ScalarType mh_squared = m_h*m_h;
//vn+1 = vn + h*f(xn,vn)
//xn+1 = xn + vn+1*h;
//update rule here is xn+1 = xn + m_h*(vn + f(xn,vn))
pos_next = m_mesh->m_current_positions + m_mesh->m_current_velocities*m_h + force*mh_squared;
}
updatePosAndVel(pos_next);
}
void Simulation::integrateExplicitEuler()
{
// q_{n+1} - 2q_n + q_{n-1} = h^2 * M^{-1} * force(q_{n-1})
// inertia term 2q_n - q_{n-1} is calculated in calculateInertiaY function
// calculate force(q_{n-1})
// VectorX position_previous = m_mesh->m_current_positions - m_mesh->m_current_velocities*m_h;
VectorX position_previous = m_mesh->m_current_positions - m_mesh->m_current_velocities*m_h;
VectorX force_previous;
computeForces(position_previous, force_previous);
//cout<<force_previous<<endl;
// update q_{n+1}
ScalarType h_square = m_h*m_h;
VectorX pos_next = m_inertia_y + h_square*m_mesh->m_inv_mass_matrix*force_previous;
//cout<<"pos_next"<<pos_next.block_vector(0)<<endl;
//cout<<"m_current"<<m_mesh->m_current_positions.block_vector(0)<<endl;
updatePosAndVel(pos_next);
}
