@article{Kenwright2012,
abstract = {This paper presents an overview of the analytical advantages of dual-quaternions and their potential in the areas of robotics, graphics, and animation. While quaternions have proven themselves as providing an unambiguous, un-cumbersome, computationally efficient method of representing rotational information, we hope after reading this paper the reader will take a parallel view on dual-quaternions. Despite the fact that the most popular method of describing rigid transforms is with homogeneous transformation matrices they can suffer from several downsides in comparison to dual-quaternions. For example, dual-quaternions offer increased computational efficiency, reduced overhead, and coordinate invariance. We also demonstrate and explain how, dual-quaternions can be used to generate constant smooth interpolation between transforms. Hence, this paper aims to provide a comprehensive step-by-step explanation of dual-quaternions, and it comprising parts (i.e., quaternions and dual-numbers) in a straightforward approach using practical real-world examples and uncomplicated implementation information. While there is a large amount of literature on the theoretical aspects of dual-quaternions there is little on the practical details. So, while giving a clear no-nonsense introduction to the theory, this paper also explains and demonstrates numerous workable aspect using real-world examples with statistical results that illustrate the power and potential of dual-quaternions.},
author = {Kenwright, Ben},
keywords = {blending,dual-number,dual-quaternion,interpolation,introduction,quaternion,transformation,why should we use},
number = {October},
pages = {1--11},
title = {{Dual-Quaternions From Classical Mechanics to Computer Graphics and Beyond}},
url = {www.xbdev.net},
year = {2012}
}
@article{Nguyen1988,
author = {Nguyen, V.-D.},
doi = {10.1177/027836498800700301},
issn = {0278-3649},
journal = {The International Journal of Robotics Research},
month = jun,
number = {3},
pages = {3--16},
title = {{Constructing Force- Closure Grasps}},
url = {http://ijr.sagepub.com/cgi/doi/10.1177/027836498800700301},
volume = {7},
year = {1988}
}
@book{Hairer1996,
author = {Hairer, E and N\o rsett, S P and Wanner, G},
isbn = {9783540604525},
publisher = {Springer},
series = {Lecture Notes in Economic and Mathematical Systems},
title = {{Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems}},
url = {http://books.google.de/books?id=m7c8nNLPwaIC},
year = {1996}
}
@article{Lowe2004,
abstract = {This paper presents a method for extracting distinctive invariant features from images that can be used to perform reliable matching between different views of an object or scene. The features are invariant to image scale and rotation, and are shown to provide robust matching across a a substantial range of affine distortion, change in 3D viewpoint, addition of noise, and change in illumination.},
author = {Lowe, David G.},
doi = {10.1023/B:VISI.0000029664.99615.94},
issn = {0920-5691},
journal = {International Journal of Computer Vision},
keywords = {SIFT},
mendeley-tags = {SIFT},
month = nov,
number = {2},
pages = {91--110},
title = {{Distinctive Image Features from Scale-Invariant Keypoints}},
url = {http://link.springer.com/10.1023/B:VISI.0000029664.99615.94},
volume = {60},
year = {2004}
}