A beginners guide to dual-quaternions: What they are, how they work, and how to use them for 3D character hierarchies

Research output: Chapter in Book/Report/Conference proceedingConference contribution

24 Citations (Scopus)

Abstract

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.

Original languageEnglish
Title of host publication20th International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision
Pages1-10
Number of pages10
Publication statusPublished - 2012
Event20th International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision 2012 - Plzen, Czech Republic
Duration: 26 Jun 201228 Jun 2012

Conference

Conference20th International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision 2012
Abbreviated titleWSCG 2012
CountryCzech Republic
CityPlzen
Period26/06/1228/06/12

Keywords

  • 3D
  • Character hierarchies
  • Dual-quaternion
  • Real-time
  • Rigid transformation

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Computer Vision and Pattern Recognition

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    Kenwright, B. (2012). A beginners guide to dual-quaternions: What they are, how they work, and how to use them for 3D character hierarchies. In 20th International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision (pp. 1-10)