对偶四元数综述
A Survey on Dual-Quaternions
摘要：
在过去的几年里，对偶四元数的应用不仅在许多不同的方向上发展，而且在几个领域也以令人兴奋的方式发展。由于对偶四元数提供了一种高效而紧凑的符号形式，具有独特的数学性质。虽然双四元数现在在研究和实现的许多方面都很常见，例如机器人和工程到计算机图形和动画，但仍然有大量的探索途径，具有巨大的潜在利益。这篇文章是第一个提供一个全面的审查双四元数景观。在这次调查中，我们提出了一个审查的双四元数技术和多年来开发的应用，同时提供洞察当前和未来的发展方向。本文首先介绍了双四元数的定义，它们的数学公式，同时解释了重要的关键方面（例如，压缩和模糊性）。本文中的文献综述分为几类，以帮助管理和可视化双四元数在解决特定问题时的应用。一个时间轴说明关键的方法，解释如何双四元数的方法已经取得了进展，多年来。讨论了最流行的双四元数方法在文献中的影响，性能，计算成本和现实世界的结果（与相关模型相比）。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。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
