Results 31 to 40 of about 1,033 (257)
Pose-Following with Dual Quaternions
2023 62nd IEEE Conference on Decision and Control (CDC), 2023 This work focuses on pose-following, a variant of path-following in which the goal is to steer the system's position and attitude along a path with a moving frame attached to it. Full body motion control, while accounting for the additional freedom to self-regulate the progress along the path, is an appealing trade-off.
Jon Arrizabalaga, Markus Ryll
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CoRR, 2023 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 their advantages and disadvantages.
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Dual Quaternion Embeddings for Link Prediction
Applied Sciences, 2021 The applications of knowledge graph have received much attention in the field of artificial intelligence. The quality of knowledge graphs is, however, often influenced by missing facts.
Liming Gao +3 more
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Functional Calculus for Dual Quaternions
Advances in Applied Clifford Algebras, 2023 We give a formula for $f(η)$, where $f :\mathbb C \to \mathbb C$ is a continuously differentiable function satisfying $f(\bar z) = \overline{f(z)}$, and $η$ is a dual quaternion. Note this formula is straightforward or well known if $η$ is merely a dual number or a quaternion.
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A new proof of the generalized Hamiltonian–Real calculus [PDF]
Royal Society Open Science, 2016 The recently introduced generalized Hamiltonian–Real (GHR) calculus comprises, for the first time, the product and chain rules that makes it a powerful tool for quaternion-based optimization and adaptive signal processing.
Dongpo Xu, Hua Gao, Danilo P. Mandic
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A dual quaternion algorithm of the Helmert transformation problem
Earth, Planets and Space, 2018 Rigid transformation including rotation and translation can be elegantly represented by a unit dual quaternion. Thus, a non-differential model of the Helmert transformation (3D seven-parameter similarity transformation) is established based on unit dual ...
Huaien Zeng +3 more
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Dual-Quaternion Fourier Transform
CoRR, 2023 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 into a form that describes the frequencies.
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On tertions and dual numbers [PDF]
Notes on Number Theory and Discrete MathematicsIn a previous author's paper [1], the mathematical object called "tertion" was discussed. Some operations over tertions were introduced and their properties were studied. There, it was showed that the complex numbers and quaternions can be represented by
Krassimir T. Atanassov
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IEEE Access, 2020 This paper aims to construct signal sets from quotient rings of the quaternion over a real number field associated with the arithmetic Fuchsian group Γ4g, where g is the genus of the associated surface.
Catia Regina de Oliveira Quilles Queiroz +1 more
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