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 which will multiply the system matrix so that: . This projection matrix 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 indice 5:

By projecting this matrix on the right hand side vector we have . This ensures to have the projection , 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();
        }
    }
}

Data

The FixedProjectiveConstraint can be initialized using three input data:

• indices: corresponding to the indices of the fixed points
• fixAll: filters all the DOF to implement a fixed object
• activate_projectVelocity: if true, projects not only a constant but a zero velocity

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.

Example

This component is used as follows in XML format:

<FixedProjectiveConstraint name="FixedProjectiveConstraint" indices="3 39 64" />

or using SofaPython3:

node.addObject('FixedProjectiveConstraint', indices='3 39 64')

An example scene involving a FixedProjectiveConstraint is available in examples/Component/Constraint/Projective/FixedProjectiveConstraint.scn