Rigid3d Tutorial -

// Rotation: 90 deg around Z Quaterniond q = Quaterniond(Eigen::AngleAxisd(M_PI/2, Vector3d::UnitZ())); Vector3d t(1.0, 0.0, 0.0); SE3d T_ab(q, t); // Transformation from frame A to frame B

T_ac = T_ab @ T_bc Order matters. The rightmost transform is applied first to the point. 6. Inversion The inverse of a rigid transform ( T_ab ) is ( T_ba ). It rotates by ( R^T ) and translates by ( -R^T t ). rigid3d tutorial

[ p_B = R_AB \cdot p_A + t_AB ]