A Beginners Guide to Dual-Quaternions
双四元数理论教程dual-quaternion
In this paper, we give a beginners guide to the practicality of using dual-quaternions to represent the rotations
and translations in character-based hierarchies. Quaternions have proven themselves in many fields of science
and computing as providing an unambiguous, un-cumbersome, computationally efficient method of representing
rotational information. We hope after reading this paper the reader will take a similar view on dual-quaternions.
We explain how dual number theory can extend quaternions to dual-quaternions and how we can use them to
represent rigid transforms (i.e., translations and rotations). Through a set of examples, we demonstrate exactly
how dual-quaternions relate rotations and translations and compare them with traditional Euler’s angles in
combination with Matrix concatenation. We give a clear-cut, step-by-step introduction to dual-quaternions,
which is followed by a no-nonsense how-to approach on employing them in code. The reader, I believe, after
reading this paper should be able to see how dual-quaternions can offer a straightforward solution of
representing rigid transforms (e.g., in complex character hierarchies). We show how dual-quaternions propose a
novel alternative to pure Euler-Matrix methods and how a hybrid system in combination with matrices results in
a faster more reliable solution. We focus on demonstrating the enormous rewards of using dual-quaternions for
rigid transforms and in particular their application in complex 3D character hierarchies.
