Over the past few years, the applications of dual-quaternions have not only developed in many different directions but has also evolved in exciting ways in several areas. As dual-quaternions offer an efficient and compact symbolic form with unique mathematical properties. While dual-quaternions are now common place in many aspects of research and implementation, such as, robotics and engineering through to computer graphics and animation, there are still a large number of avenues for exploration with huge potential benefits. This article is the first to provide a comprehensive review of the dual-quaternion landscape. In this survey, we present a review of dual-quaternion techniques and applications developed over the years while providing insights into current and future directions. The article starts with the definition of dual-quaternions, their mathematical formulation, while explaining key aspects of importance (e.g., compression and ambiguities). The literature review in this article is divided into categories to help manage and visualize the application of dual-quaternions for solving specific problems. A timeline illustrating key methods is presented, explaining how dual-quaternion approaches have progressed over the years. The most popular dual-quaternion methods are discussed with regard to their impact in the literature, performance, computational cost and their real-world results (compared to associated models). Finally, we indicate the limitations of dual-quaternion methodologies and propose future research directions.
翻译:近几年,双四元数的应用不仅在许多不同方向上得以发展,而且在多个领域以令人兴奋的方式发展。双四元数提供了一种高效紧凑的符号形式,具有独特的数学性质。虽然双四元数现在在许多研究和实现方面已经司空见惯,例如机器人和工程,甚至到计算机图形和动画,但仍有很多探索的方向,有巨大的潜在好处。本文是第一篇全面综述双四元数应用领域的文章。在这篇综述中,我们介绍了多年来开发的双四元数技术和应用,同时提供对当前和未来方向的见解。文章首先介绍双四元数的定义和数学形式,同时解释了重要方面的关键性(例如,压缩和模糊度)。本文中的文献综述被分为类别,以帮助管理和可视化双四元数应用于解决特定问题的情况。提供了一个时间线,说明了双四元数方法如何随着时间的推移而发展。讨论了最受欢迎的双四元数方法,针对其在文献中的影响、性能、计算成本以及与相关模型的实际结果进行了讨论。最后,我们指出了双四元数方法的局限性并提出了未来的研究方向。