 Since the space of dual quaternions is 8-dimensional and a rigid transformation have six real degrees of freedom, three for translations and three for rotations, dual quaternions obeying two algebraic constraints are used in this application.Similar to the way that rotations in 3d space can be represented by quaternions of unit length, rigid motions in 3d space can be represented by dual quaternions of unit length.This fact is used in theoretical kinematics (see McCarthy), and in applications to 3D computer graphics, robotics and computer vision.