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 ).
p_a = np.array([0, 1, 0]) p_b = T[:3,:3] @ p_a + T[:3,3] print(p_b) # [0., 0., 0.] If you have ( T_bc ) and ( T_ab ), the transform from ( a ) to ( c ) is: rigid3d tutorial
In robotics, computer vision, and 3D graphics, the ability to represent rotations and translations in 3D space is fundamental. The Rigid3D object (often found in libraries like Sophus , Eigen , geometry_msgs , or tf2 ) is the industry-standard way to do this. Unlike a 4x4 homogeneous matrix, Rigid3D separates rotation (SO(3)) and translation, offering better numerical stability and mathematical clarity. T_ac = T_ab @ T_bc Order matters
[ p_B = R_AB \cdot p_A + t_AB ]
[ T_ac = T_ab \cdot T_bc ]
