FixedProjectiveConstraint

This component belongs to the category of Projective Constraint. The FixedProjectiveConstraint projects a constant velocity. If the fixed points have a zero velocity at the simulation start, they will keep a zero velocity i.e. be fixed.

As introduced in the page about the Projective Constraint, the FixedProjectiveConstraint corresponds to a projection matrix noted \(\mathbf{P}\) which will multiply the system matrix \(\mathbf{A}\) so that: \(\mathbf{P}^T\mathbf{A}\mathbf{P}\Deltav=\mathbf{P}^Tb\). This projection matrix \(\mathbf{P}\) is the identity matrix in which the diagonal value corresponding to the indices of the fixed points equals zero. These lines and columns equals 0. As a consequence, when the integration scheme (ODESolver) will call the projectResponse() or projectVelocity() the constraint will be applied, ensuring that the desired degrees of freedom remain fixed.

Example of a system of size 6, with a fixed constraint at the index 5:

\[ \mathbf{P}=\begin{bmatrix}1&0&0&0&0&0\\0&1&0&0&0&0\\0&0&1&0&0&0\\0&0&0&1&0&0\\0&0&0&0&\mathbf{0}&0\\0&0&0&0&0&1\end{bmatrix} \]

By projecting this \(\mathbf{P}\) matrix on the right hand side vector we have \(\mathbf{P}^Tb\). This ensures to have the projection \(b[5]=0\), thus preventing any time evolution of the fifth degree of freedom. In such case, we function projectResponse():

template <class DataTypes>
void FixedProjectiveConstraint<DataTypes>::projectResponse(const core::MechanicalParams* mparams, DataVecDeriv& resData)
{
    SOFA_UNUSED(mparams);

    helper::WriteAccessor<DataVecDeriv> res (resData );
    const SetIndexArray & indices = d_indices.getValue();

    if( d_fixAll.getValue() )
    {
        // fix everything
        typename VecDeriv::iterator it;
        for( it = res.begin(); it != res.end(); ++it )
        {
            *it = Deriv();
        }
    }
    else
    {
        for (SetIndexArray::const_iterator it = indices.begin(); it != indices.end(); ++it)
        {
            res[*it] = Deriv();
        }
    }
}

Usage

The FixedProjectiveConstraint requires a MechanicalObject to store the degrees of freedom associated to the nodes, as well as a Mass so that the system matrix is not null. An integration scheme and a solver are also necessary to solve the linear system at each time step.

Note that if only a part of the degrees of freedom must be constraint, you can use the PartialFixedProjectiveConstraint working in the same way as the FixedProjectiveConstraint.