T_ba = np.linalg.inv(T_ab) # For rigid transforms, this is more efficient: R_inv = T_ab[:3,:3].T t_inv = -R_inv @ T_ab[:3,3] C++:
SE3d T_ba = T_ab.inverse();
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
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 ). T_ba = np