Incremental Spherical Linear Interpolation

Animation is often done by setting up a sequence of key orientations, represented by quaternions. The in between orientations are obtained by spherical linear interpolation (SLERP) of the quaternions, which then can be used to rotate the objects. However, SLERP involves the computation of trigonometric functions, which are computationally expensive. Since it is often required that the angle between each quaternion should be the same, we propose that incremental SLERP is used instead. In this paper we demonstrate five different methods for incremental SLERP, whereof one is new, and their pros and cons are discussed.