Eigen, rotate a vector3d with a quaternion?

I have an array of 3D points, as a std::vector<Eigen::Vector3d>.

I need to transform these points with a position and quaternion.

My questions are:

How can I rotate these points with a quaternion? And is there a faster way than:

Eigen::Vector3d Trans;     // position to move by
Eigen::Quaterniond quats;  // quat to rotate by

for (int p = 0; p < objectPoints.size(); p++) {
    Eigen::Vector3d pnt;
    // add pose
    pnt.x = objectPointsTri[p].x + -Trans.x();
    pnt.y = objectPointsTri[p].y + -Trans.y();
    pnt.z = objectPointsTri[p].z + -Trans.z();

    Eigen::Vector3d pntRot =  // rotate pnt by the quaternion
}

Operator * will do the job, and you can of course simplify your code:

pnt = objectPointsTri[p] - Trans;
pntRot = quat * pnt;

or even:

pnt = quat * (objectPointsTri[p] - Trans);

or, if you store your points in a Matrix3Xd:

Matrix3Xd in_pts;
Matrix3Xd out_pts;
Affine3d T = quats * Translation3d(-Trans);
out_pts = T * in_pts;