Related papers: A Survey on Dual-Quaternions
Dual quaternion algebra and its application to robotics have gained considerable interest in the last two decades. Dual quaternions have great geometric appeal and easily capture physical phenomena inside an algebraic framework that is…
Transformations in the field of computer graphics and geometry are one of the most important concepts for efficient manipulation and control of objects in 2-dimensional and 3-dimensional space. Transformations take many forms each with…
Fourier transform (FT) plays a crucial role in a broad range of applications, from enhancement, restoration and analysis through to security, compression and manipulation. The Fourier transform (FT) is a process that converts a function…
This paper presents an experimental study on the application of quaternions in several machine learning algorithms. Quaternion is a mathematical representation of rotation in three-dimensional space, which can be used to represent complex…
Numerous attempts have been made to replicate the success of complex-valued algebra in engineering and science to other hypercomplex domains such as quaternions, tessarines, biquaternions, and octonions. Perhaps, none have matched the…
We explain the use of dual quaternions to represent poses, twists, and wrenches.
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…
Dual quaternions have gained significant attention due to their wide applications in areas such as multi-agent formation control, 3D motion modeling, and robotics. A fundamental aspect in dual quaternion research involves the projection…
Quaternions, discovered by Sir William Rowan Hamilton in the 19th century, are a significant extension of complex numbers and a profound tool for understanding three-dimensional rotations. This work explores the quaternion's history,…
Solving dual quaternion equations is an important issue in many fields such as scientific computing and engineering applications. In this paper, we first introduce a new metric function for dual quaternion matrices. Then, we reformulate…
The attitude space has been parameterized in various ways for practical purposes. Different representations gain preferences over others based on their intuitive understanding, ease of implementation, formulaic simplicity, and physical as…
Objects' rigid motions in 3D space are described by rotations and translations of a highly-correlated set of points, each with associated $x,y,z$ coordinates that real-valued networks consider as separate entities, losing information.…
Quaternions are an important tool to describe the orientation of a molecule. This paper considers the use of quaternions in matching two conformations of a molecule, in interpolating rotations, in performing statistics on orientational…
Optimization models involving quaternion matrices are widely used in color image process and other engineering areas. These models optimize real functions of quaternion matrix variables. In particular, $\ell_0$-norms and rank functions of…
As an expansion of complex numbers, the quaternions show close relations to numerous physically fundamental concepts. In spite of that, the didactic potential provided by quaternion interrelationships in formulating physical laws are hardly…
In the last one and a half centuries, the analysis of quaternions has not only led to further developments in mathematics but has also been and remains an important catalyst for the further development of theories in physics. At the same…
We study matrix forms of quaternionic versions of the Fourier Transform and Convolution operations. Quaternions offer a powerful representation unit, however they are related to difficulties in their use that stem foremost from…
Dual quaternions and dual quaternion matrices have garnered widespread applications in robotic research, and its spectral theory has been extensively studied in recent years. This paper introduces the novel concept of the dual complex…
This is part two of a series of four methodological papers on (bi)quaternions and their use in theoretical and mathematical physics: 1- Alphabetical bibliography, 2- Analytical bibliography, 3- Notations and terminology, and 4- Formulas and…
Multidimensional quaternion arrays (often referred to as "quaternion tensors") and their decompositions have recently gained increasing attention in various fields such as color and polarimetric imaging or video processing. Despite this…