Applications of Dual Quaternions in Three Dimensional Transformation and Interpolation

Quaternions have long been integral to the field of computer graphics, due to their minimal and robust representation of rotations in three dimensional space. Dual quaternions represent a compact method of representing rigid body transformations (that is rotations and translations) with similar interpolation and combination properties. By comparing them to two other kinds of rigid transformations, we examine their properties and evaluate their usefulness in a real time environment. These properties include accuracy of operations, efficiency of operations, and the paths that interpolation and blending methods using those transformation methods take. The blending and interpolation methods are of particular interest as we constructed a skeletal animation system to highlight a potential application of dual quaternions. The bone hierarchy was constructed with dual quaternions and a sequence of identical hierarchies with different transformations at each bone can be interpolated as though they were keyframes to produce animations. Weighted transformations required in skinning the skeleton structure to a triangular mesh also prove an effective application of dual quaternions. Our findings show that while dual quaternions are useful in the context of skeletal animation, other applications may favour other representations, due to simplicity or speed.