A dual quaternion is a mathematical structure that extends the concept of quaternions to represent both rotation and translation in three-dimensional space. It consists of a real part and a dual part, allowing it to encode transformations in a compact form. This makes dual quaternions particularly useful in computer graphics and robotics for smoothly interpolating movements. In a dual quaternion, the real part represents rotation, while the dual part captures translation. This combination enables efficient calculations for tasks like 3D animation and robot motion planning, where both orientation and position changes are essential. By using dual quaternions, developers can simplify complex transformations and improve computational efficiency.