Dual-Quaternion Interpolation

Transformations in the field of computer graphics and geometry are one of the most important concepts for efficient manipulation and control of objects in 2-dimensional and 3-dimensional space. Transformations take many forms each with their advantages and disadvantages. A particularly powerful tool for representing transforms in a unified form are dual-quaternions. A benefit of this unified form is the interpolation properties, which address a range of limitations (compact form that allows a rotational and translational components to be coupled). In this article, we examine various dual-quaternion interpolation options that achieve different trade-offs between computational cost, aesthetic factors and coupling dependency. Surprisingly, despite dual-quaternions being a common tool in graphics libraries, there are limited details on the interpolation details. Here we attempt to explain interpolation concept, elaborating on underpinning theories, while explaining concepts and bespoke modifications for added control.