PDF - Dual Quaternions Paper

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.


Keywords: dual-quaternions, rigid transformation, dual quaternion, transformation, blending, rigid body motion, introduction, implementation

Title: A Beginners Guide to Dual-Quaternions: What They Are, How They Work, and How to Use Them for 3D Character Hierarchies
Authors: Ben Kenwright
Publication date: 2012/6
Journal name: The 20th International Conference on Computer Graphics, Visualization and Computer Vision
WSCG 2012 Communication Proceedings
Pages: 1-13
Publisher: http://www.wscg.eu/