There is a good tutorial in the Eigen docs: here
In your case, this should look like:
Eigen::Vector3f trans_vec_A;
//note that you have to create a Translation because multiplying a
//Transform with a vector will _apply_ the transform to the vector
Eigen::Translation<float,3> translation_A(trans_vec_A);
Eigen::Quaternionf rotation_B;
Eigen::Quaternionf rotation_C;
Eigen::Quaternionf rotation_D;
Eigen::Vector3f trans_vec_E;
Eigen::Translation<float,3> translation_E(trans_vec_E);
Eigen::Transform<float,3,Affine> combined =
translation_A * rotation_B * rotation_C * rotation_D * translation_E;
Note that
combined = A*B*C*D*E
so combined
applied to a vector v
is
combined*v = A*B*C*D*E*v = A*(B*(C*(D*(E*v))))
that is, E
is applied first, then D
, and so on. In my mind, this is the correct order, but that may be a matter of taste.