Dual quaternion
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In ring theory, dual quaternions are a non-commutative ring constructed in the same way as the quaternions, except using dual numbers instead of real numbers as coefficients. A dual quaternion can be represented in the form q = q0 + ε qε, where q0 and qε are ordinary quaternions and ε is the dual unit.
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 applications to 3D computer graphics and robotics.
