Double quaternions for motion interpolation

Abstract

This paper describes the concept of double quaternions, an extension of quaternions, and shows how they can be used for effective three-dimensional motion interpolation. Motion interpolation using double quaternions has several advantages over the method of interpolating rotation and translation independently and then combining the results. First, double quaternions provide a conceptual framework that allows one to handle rotational and translational components in a unified manner. Second, results obtained by using double quaternions are coordinate frame invariant. Third, double quaternions allow a natural way to tradeoff robustness against accuracy. Fourth, double quaternions, being a straightforward extension of quaternions, can be integrated into several existing systems that currently use quaternions with translational components, with a only small coding effort.